Ch2_exercise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a40d7e02",
   "metadata": {},
   "source": [
    "<center><h2>Exercise for Chapter 2: Path and Curves</h2></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01cfc523",
   "metadata": {},
   "source": [
    "<h3>Section 1: Parametrizations</h3>\n",
    "\n",
    "<b>In exercise 1.1 - 1.8 sketch the curve parametrized by the given path. Indicate on the curve the direction in which it is being traversed.</b>\n",
    "\n",
    "<b>1.1</b> $\\alpha: [0,2] \\to \\mathbb{R}^2, \\alpha(t) = (t, t^2)$\n",
    "\n",
    "<b>1.2</b> $\\alpha: [0, 6\\pi] \\to \\mathbb{R}^2, \\alpha(t) = (t cos \\,t, t sin \\,t)$\n",
    "\n",
    "<b>1.3</b> $\\alpha :\\mathbb{R} \\to \\mathbb{R}^2, \\alpha(t) = (e^t, e^{-t})$ (Hint: How are the $x$ and $y-$coordinates related?)\n",
    "\n",
    "<b>1.4</b> $\\alpha : \\mathbb{R} \\to \\mathbb{R}^3, \\alpha(t) =  (cos \\,t, sin \\,t, t)$\n",
    "\n",
    "<b>1.5</b> $\\alpha : \\mathbb{R} \\to \\mathbb{R}^3, \\alpha(t) = (cos \\,t, sin \\,t, -t)$\n",
    "\n",
    "<b>1.6</b> $\\alpha : \\mathbb{R} \\to \\mathbb{R}^3, \\alpha(t) = (sin \\,t, cos \\,t, t)$\n",
    "\n",
    "<b>1.7</b> $\\alpha : \\mathbb{R} \\to \\mathbb{R}^3, \\alpha(t) = (sin \\,t , cos \\,t, -t)$\n",
    "\n",
    "<b>1.8</b> $\\alpha : [0, 2\\pi] \\to \\mathbb{R}^3, \\alpha(t) = (cos \\,t, sin \\,t, cos \\,2t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "44cec3b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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61F27dmXZsmXUqVMHgMOHD1OhQoYTrgEQEhJCWFhYhvtk1apV2X5fhw8fpm7djC4i7xtbtmxh9OjRLFq06KLlFStW5NChQ5rQA8SKfSt46/e3ePWGV6lVVs8BCBQBm9DtUL9+febMmZPhusKFC5OSkpL2PP3YZ/fpMvv378+tt97KzTffjDGGK6+8ktjYWOrXr88vv/ySo5hSW6klS5akSZMmacuLFi3qcfz1uXPnCA8Pv2R5Tlro2anHW+Li4ujTpw+ffPIJtWvXvmhdUlISRYsW9UscKmuJjkSeW/kc245to3AhTSGBRA+KuunQoQPnzp1jypQpacs2bdrEqlWrqFmzJlu3buXcuXOcOnWKpUuXZlpO7dq1CQkJ4fnnn09rudepU4djx46lJXSHw8GWLVuyjKdZs2asXr0agDlz5lx0kLFu3brs2rUr7XloaCgOhyPt+YkTJyhfvnyGp8SvWrWKDRs2XHJLn8wzqqdkyZIX/TMYM2YMX3/99SWvS7+dJ6dOnaJHjx5MmDCBVq1aXbRORPj777/x9vz5Kuf2nNxDvbfrsWzvMupWqEv10tXtDkm50YTuxhjD119/zZIlS6hduzb169dnzJgxVKpUierVq9OvXz+ioqLo16/fRa3ljPTv358ZM2bQr18/wBp5MmfOHEaPHk2jRo1o3LhxWp/ye++9l9aP7m7kyJH8+uuv3HjjjSQlJdGlSxceeOABAHr06EFMTEzatsOGDaNhw4bcdtttACxfvpwePXrkeZ9069aNlStXpj0fOnQow4cPp3Hjxvz777/ExsZSqVKlS143YMAAXn31VZo0acLu3bs91jN58mR27drFc889R+PGjWncuDFHjx4FYN26dbRs2ZLChbU1aJc1B9cwbcM0Tp87zf7T1nTcsUdi+f3g7zZHpi6S2dHS9DcgBPgDmJ/BuiLAbGAX8BsQ6ak8T6NcciM3ozjyq8TERLnmmmskOTk5w/V9+vSRHTt2XLQst/vnpptukp07d2a4rnPnzrkqMydGjhwpS5YsyXS9jnLxrYTzCXLlixHCOGTizInCOIRxSOupreVfx792hxdw7BzlkpMW+kNAZlP13QWcFJErgDeA/8vVfxeVbUWLFmX8+PEcPHjwknXnz5/npptu4qqrrvJKXRMmTODw4cMZrstspIo3RUVF0bFjR5/XozL24Fvd+Tv+CPxbhrOnLxzHOH/kEOeSz9kYmUovWwndGFMN6AF8mMkmvYHUs0TmAB2NTrLhc126dKFGjRqXLA8LC+P222/3Wj116tShbdu2Xisvp+655x7b6lbw6nu7Wfc+dJszmPEj7oNFrwBw8J/97Du1z97g1EWy2yk5CXgcyGxMYFXgAICIJBtjTgPlgOPuGxljhgHDACIiIi7qAwZrvu6cHEhLz+l05un1wS5Y909SUtIln6Xcio+P91pZQePehwE4O/1GAO64qiFNak8kPBlObj9JzPYY+2ILQLZ+hjLri5EL/eM9gXdcj9uRcR/6ZqCa2/PdQPmsytU+dP8L1v2jfeg+VrOmJBkjhcKPCYjs4nLZXwq54r+F5XTSabujCziB3ofeCuhljNkHzAI6GGNmpNvmIFAdwBhTGCgNnMjTfxqlVGB48UUWlW9KSlJ5KpQ+y+XsoUZyMXY2/ZhSRUrZHZ1y4zGhi8gYEakmIpHAAGCZiAxOt9k84A7X476ubXJxrqf9QkJC0obNNW7cmAkTJuTo9ZGRkRw/ftzzhhm4++67M5yh0F1msxgq5SvOgQP4ot3jADS+4i9MzZowZQpmcPo0oOyW64G9xpjnsJr+84CPgE+NMbuAf7ASf75UtGjRi+ZE8acPP8zsmPMF33zzDT179qRevXp+iEgpeH/d+8yItc41aNwhBF7ZZ29AKlM5OrFIRGJEpKfr8bOuZI6IJInIrSJyhYi0EJE9vgj2Ep99BpGRUKgQREZS+IsvfFZVZGQkY8eOpWnTpjRo0IDt27cD1hmZnTt3pn79+tx9992pxxDYt28fV199Nbfddht169alb9++JCYmArB06VKaNGlCgwYNuPPOOzl3zhr61a5dO9auXQtAiRIleOqpp2jUqBEtW7bkyJEj/Pzzz8ybN49Ro0bRuHFjdu/ezZtvvkm9evVo2LAhAwbk2/+jKkCJCDde2ZuyR28CoEmTU7bGo7KWf88U/ewzGDYM9u+3ZvLav5/wBx+0lufBv//+e1GXi/uc4uXLl2f9+vWMGDGCiRMnAjB+/Hhat27Nli1b6NOnD3/99Vfa9jt27OC+++5j27ZtlCpVinfeeYekpCSGDh3K7NmziY2NJTk5mXffffeSOBISEmjZsiUbN26kbdu2fPDBB2mzGL766qts2LCB2rVrM2HCBP744w82bdqU4dmmSuXF6CWjqfPMrZz8pxA1akClSnr91kCWfxP6U0+Bq8Wbyvz7r7U8D1K7XFJv7rMo3nzzzQBER0ezb98+AFauXMlgV19ijx49KFu2bNr21atXT5uXZPDgwfz000/s2LGDWrVqpZ30c8cdd1x0an2qsLAwevbseUl96aWe7j9jxgw9NV55Xavqrbij9DQA2rcHPbsksOXfhO7WEs7Wci9InfkwJCQkW5d3S39uVU7OtQoNDU3bPqv6vv/+e+6//37Wr19P8+bNvXbZOaXeXfsuRxKOcHCT1fho397mgJRH+TehZ3CGZJbLfaRt27bMnDkTgB9++OGia1/+9ddfabMrzpw5k9atW1OnTh327duXNoPhp59+yvXXX5/t+txnMUxJSeHAgQO0b9+e//u//+P06dPEx8d7662pAu79te9zIv4UqT8gNaEHvvyb0F98EYoVu2iRFC1qLc+D9H3oTzzxRJbbjx07lpUrV1K/fn2++uqri07Fr1OnDm+//TZ169bl5MmTjBgxgvDwcD7++GNuvfVWGjRoQKFChTK9wEVG3Gcx/PPPPxk8eDANGjSgSZMmjBw5kjJlyuT2rSuVZsfxHXwz4BtuKP44p0/D5Zf7va2kciOzM458ffPKmaIzZojUrClijEjNmpL44Yc5e70P7d27N8vrYNpBzxT1TM8UFUl2JgvjkPfXvi+vvGJdi/euu6x1un8802uK5tZtt1k3l+QgnKdEKTus+s8qWtdoTfdnrOfa3ZI/5N8ulwAXGRnJ5s2b7Q5DqRxxOB0Ufr4wl4VfhsOB9p/nM5rQlVJpTiadpH/9/lxd4WrWrIGEBLj6aqhSxe7IVHZoQldKAVbrfOLPE5naayqFTCGWL7eWa+s8/9CErpQCYPGexbz686uEh4YDsGyZtbxDBxuDUjmiCV0phYhQo3QNzj99nkKmEElJ4LqGOTk4TULZTBN6OqnT59avX59GjRrx2muvkZKSAsDatWsZOXKkV+p56aWXLnp+3XXXeaXczGzfvp1WrVrRpEkTdu/enbb8mmuuoXHjxtSoUYMKFSqkjb/PbKoBOw0dOpQ5c+bYHUZQGhszlgbvNiA0JBSAX36BpCRo1AgqVLA5OJVtAT1sMWZfDGOWjqFkWEmuq34dr/3yGsOaDuPEvyeI2RfD0MZD+W7nd1QpUYXoKtG8vOplHrn2Efad2sf6w+sZ2GAgc7fN5arLrqJBRAPGrxiPjM16mnb36XOPHj3KoEGDOHPmDOPHj6dZs2Y0a9bsktckJyfneB6Vl156iSeffDLt+c+pzSEf+eabb+jduzfPP//8Rct/++03AKZNm8batWuZPHnyRetz896yw1flqty5qc5N9KvXL+25drfkTwHdQh80dxC/xv3K4j2LGb9iPPHn43n919eZvnE6+0/vZ/yK8aw/vJ75f85n/IrxnE85z4TVE5i1ZRY7/9nJ+BXj2Xx0M19t/4rxK8Yz9vqxOaq/YsWKTJkyhcmTJyMixMTEpE2YNW7cOIYMGUKrVq0YMmQIx44d45ZbbqF58+Y0b96c1atXA9b1Bf/zn//QoEEDGjZsyNy5c3niiSfSzki9zTWOvkSJEoD103fUqFFERUXRoEGDtNkeY2JiaNeuHX379k2bllcyuIbIhg0baNmyJQ0bNqRPnz6cPHmSBQsWMGnSJD766CPaZ+MIV/r3tm/fPtq0aUPTpk1p2rRp2j+fAQMG8P3336e9LrUF7XQ6GTVqFM2bN6dhw4a8//77ae+hTZs29OrVi3r16pGQkECPHj1o1KgRUVFRae/1ueeeo3nz5kRFRTFs2LAM36fynmeWPcO7694lKiIqbdnSpdZ9x442BaVyJaCbSD2v6skH6z/wWnmxR2Jz/JrLL78cp9PJ0aNHL1m3detWfvrpJ4oWLcqgQYP473//S+vWrfnrr7/o0qUL27Zt4/nnn6d06dLExlp1nzx5kltuuYXJkydneCGNr776ig0bNrBx40aOHz9O8+bNadu2LQB//PEHW7ZsoUqVKrRq1YrVq1fTunXri15/++2389Zbb3H99dfz7LPPMn78eCZNmsTw4cMJDQ3lqWzORun+3hITE1m8eDHh4eH8+eefDBw4kLVr19K/f3+++OILevTowfnz51m6dCnvvvsuH330EaVLl2bNmjWcO3eOVq1a0blzZwDWr1/P5s2bqVWrFnPnzqVKlSpp/xROnz4NwAMPPMCzzz4LwJAhQ5g/fz433nhjtuJWOXfm3BmaVmqa9vzsWfj9dwgJgTZtbAxM5VhAJ/QiIUW8Wt7Of3Z6tbxevXpRtGhRAJYsWXLRpeHOnDlDfHw8S5YsYdasWWnL3afXzchPP/3EwIEDCQkJISIiguuvv541a9ZQqlQpWrRoQbVq1QDS+rndE/rp06c5depU2mRfd9xxB7feemue35vD4eCBBx5gw4YNhISEsHOntR+7devGQw89xLlz5/jxxx9p27YtRYsWZdGiRWzatCmtv/v06dP8+eefhIWF0aJFC2rVqgVAgwYNePTRRxk9ejQ9e/akjSt7LF++nFdeeYXExET++ecf6tevrwndR1b/tZpBDQZxTbVr0patWgVOJ7RsCaX0kqH5SkAn9JmbZ3q1vFvq3pLj1+zZs4eQkBAqVqzItm3bLlpXvHjxtMcpKSn8+uuvhIeH5znOzKRO3wvZn8I3t9zf2xtvvEFERAQbN24kJSUl7T2Gh4fTrl07Fi5cyOzZs9OumCQivPXWW3Tp0uWiMmNiYi4q96qrrmL9+vUsWLCAp59+mo4dO/L4449z3333sXbtWqpXr864ceNIStKLKviCiND649ZM6jLpooSu3S35V0D3oT/Y4kGvlvd57Oc52v7YsWMMHz6cBx54wONc5p07d+att95Ke57anXLDDTfw9ttvpy1PnV43NDQUh8NxSTlt2rRh9uzZOJ1Ojh07xsqVK2nRokW24i1dujRly5Zl1apVQM6n5s3M6dOnqVy5MoUKFeLTTz/F6XSmrevfvz8ff/wxq1atomvXrgB06dKFd999N+397dy5k4SEhEvKPXToEMWKFWPw4MGMGjWK9evXpyXv8uXLEx8fr6NafCjRkcjukbt5qOVDFy3XhJ5/BXRCj9kX49XymlZu6nGb1IOV9evXp1OnTnTu3JmxYz0fTH3zzTdZu3YtDRs2pF69emmXg3v66ac5efIkUVFRNGrUiOWu0++GDRuWdrUhd3369KFhw4Y0atSIDh068Morr1CpUqVsv8fp06czatQoGjZsyIYNG9L6ovPivvvuY/r06TRq1Ijt27df1Mru3LkzK1asoFOnToSFhQFw9913U69ePZo2bUpUVBT33ntvhr8mYmNjadGiBY0bN2b8+PE8/fTTlClThnvuuYeoqCi6dOlC8+bN8xy/upTD6aDEyyXYd3LfRcuPHYONGyE8HK691p7YVO4Zu0YQNGvWTFIviJxq27Zt1K1bN+25GW+4vub1tItsx1u/v8WgqEGcc55j/s75DIsexsLdCy8a0nhH1B3EO+MzHtL408t83f9rul/Z3d9vNWCcPXuWkiVL2h2G16X/3ORF6miiYJdwPoF3177LI9c+QiFzoV03ezYMGACdOsHixZe+rqDsn7zw9T4yxqwTkUvHTxPgfejuY8bHtRt3yXr3ZePajbskYaVfr5SyWufdPuvGV/2+uiiZg3a35HcB3eWilPK+rce2suqvVVxW7LJL1mlCz980oStVgIgIB88exPmM85LW+d69sGcPlCkDTT0fblIBKOASup4VqHJCPy858+rPr9JjZg/IYNBWauu8fXvrpCKV/wRUQg8PD+fEiRP6JVXZIiKcOHHCp2P/g4mIMDBqIAcePnBJ6xxgyRLrvlMnPwemvCagDopWq1aNuLg4jh07lqvXJyUl6Zc7C8G4f8LDw9POnlVZe3TRo/y460e23r/1knUpKRda6JrQ8y+PCd0YEw6sBIq4tp8jImPTbTMUeBU46Fo0WUQ+zGkwoaGhaaeF50ZMTAxNmjTJ9euDne6fgq1hRENa12id4bpNm+D4caheHa680s+BKa/JTgv9HNBBROKNMaHAT8aYH0Tk13TbzRaRB7wfolIqr2bGzqREWAlurntzhutTu1s6dgQPJ0WrAOaxD10s8a6noa6bdnIrlY/cv+B+9pzck+n61JOIbrjBTwEpn8jWmaLGmBBgHXAF8LaIjE63fijwMnAM2An8V0QOZFDOMGAYQERERLT7LITeEB8fnzavuLqU7h/PgnEfnXeexxhDaKHQjNefL0SvXq04dy6EuXNXc9lll84xlCoY94+3+XoftW/fPtMzRRGRbN+AMsByICrd8nJAEdfje4FlnsqKjo4Wb1u+fLnXywwmun88C7Z9dD75vDAO+WTDJ5lus3SpCIg0bOi5vGDbP77g630ErJVM8mqOhi2KyClXQu+abvkJETnnevohEJ2TcpVSvlHIFOK7gd8xuOHgTLfR4YrBw2NCN8ZUMMaUcT0uCtwAbE+3TWW3p72AiycOV0r5ncPpoPDzhalfoX6W0z+n9p9rQs//sjPKpTIw3dWPXgj4QkTmG2Oew2r6zwNGGmN6AcnAP8BQXwWslMqeIwlHaF2jNTXL1Mx0mxMnYN06CAsD15UOVT7mMaGLyCbgksHLIvKs2+MxwBjvhqaUyi2H08EXW75g6ZClGZ4VmmrZMhCBVq3AbZp7lU8F1Kn/SinvmLNtDo8uepTCIVm32XS4YnDRhK5UkBERWlZtSfyY+Cxb5yKwaJH1WBN6cNCErlSQeWrZU1z+5uUUD8u6D2XXLti/H8qVA50RIjgE1ORcSqm861y7MzfVucnjdqndLR076nS5wUJb6EoFkVdWv8KKfStoUa2Fx21Tu1u6dPFxUMpvNKErFUR+OfALJYt4vhC4w2GNcAHtPw8m2uWiVJDY8PcGXujwAvUr1ve47W+/wdmzULeuNWWuCg7aQlcqCIgITd5vQsy+mGxtn9rd0rmz72JS/qctdKWCQHJKMpuGb6JBRINsbb9woXWvCT24aAtdqXzO4XQQ9kIY/zr+zdb2J07AmjXW6f7XX+/j4JRfaUJXKp9LdCTy6LWP0qxqxlNkp7dkiXVSUevWerp/sNEuF6XyMYfTwYjvR/Bej/eyPCvUXWp3iw5XDD7aQlcqH/v94O98vvlzShTJ3hVy3E/314QefDShK5VPiQiFTCGczziz3TrfuhUOHoSICGjY0McBKr/ThK5UPvXCyhe4bup1WV68Ir0ff7Tuu3SBHLxM5ROa0JXKpwZEDeDPB/7MUUJP7T/v2jXr7VT+pAdFlcqHHl/8OBuPbGTh4IXZfk1CAqxYYbXM9XT/4KQtdKXyofLFyjO4QeYXfs7IihVw/jw0awbly/soMGUrbaErlc8s+HMBjSs1pnPtnJ3mqcMVg5+20JXKZ3rM7EHskdgcv+6HH6x77T8PXtpCVyofOZZwjLj/xlG1VNUcvW73bvjzTyhTBq65xjexKftpC12pfMLhdFBxYkV+P/h7jl+bOlzxhhugsDbjgpYmdKXyCUGYftN0el/dO8evTU3o2t0S3DShK5UPOJwOLv/f5XSq1SnbZ4WmOnfuwtWJNKEHN03oSuUD+07tI6RQCJVKVsrxa1euhMRE61T/KlV8EJwKGJrQlQpwzhQnv8b9yp6Re3LcOocLo1u6dfNyYCrgaEJXKsBNWT+F27+5PUen+LvThF5weEzoxphwY8zvxpiNxpgtxpjxGWxTxBgz2xizyxjzmzEm0ifRKlXAiAi9rurFsceO5ap1vm8fbN8OpUrBddd5Pz4VWLLzCTkHdBCRRkBjoKsxpmW6be4CTorIFcAbwP95NUqlCqjRS0Zz1eSrKF88d+fqp7bOb7gBQkO9GJgKSB4TuljiXU9DXTdJt1lvYLrr8Rygo8nt70OlVJrW1Vszb8C8XL9+wQLrXrtbCgYjkj43Z7CRMSHAOuAK4G0RGZ1u/Wagq4jEuZ7vBq4RkePpthsGDAOIiIiInjVrllfeRKr4+HhKlMjelVsKIt0/ngXSPjqWeAyDoXyx3LXOz58vRK9erTh3LoQvv/yZ8uXP5zmmQNo/gcrX+6h9+/brRCTjC8iKSLZvQBlgORCVbvlmoJrb891A+azKio6OFm9bvny518sMJrp/PAukfdTkvSYyYdWEXL/+xx9FQKRJE+/FFEj7J1D5eh8BayWTvJqjk4BF5JQxZjnQ1ZXEUx0EqgNxxpjCQGngRE7KVkpdsP34dr7q/xWRZSJzXUZqd0v37t6JSQW+7IxyqWCMKeN6XBS4AdiebrN5wB2ux32BZa7/JEqpHHKmOKn7dl0W7V6Up3I0oRc82WmhVwamu/rRCwFfiMh8Y8xzWE3/ecBHwKfGmF3AP8AAn0WsVAHw039+olWNVrl+/c6dsGsXXHaZzq5YkHhM6CKyCWiSwfJn3R4nAbd6NzSlCh6H00HYC2FsHrHZ88ZZ+P57675rVwgJ8UJgKl/QM0WVCiCnkk4xMGogdSvUzVM58+db9z16eCEolW9oQlcqQDicDl5Z/Qof3vhhrs4KTXXmjDUhV6FCOrtiQaMJXakAsWTPEib+MpHw0PA8lbN4MSQnw7XXWn3oquDQhK5UABARqpeqzvmnz+epdQ4X+s+1u6Xg0YSuVAAYGzOWBu81IDQkbxOupKRcSOg33uiFwFS+ogldqQDQ5+o+eR7ZArBuHRw9CjVqQP36XghM5St6uVilbPbMsmc4HH+YD3t9mOeyUke39OwJOj1ewaMtdKVsFn8+nmZVMp5rKafcE7oqeLSFrpSNfvrrJ/pH9adltfSXGMi5gwdh/XooWhTatct7bCr/0Ra6UjYREdp83Ibf4n7zSnmpB0NvuMFK6qrg0Ra6UjZJdCSye+RuLi97uVfK++47615HtxRc2kJXygYOp4MSL5dg78m9XikvMRGWLLEe6/jzgksTulI2cKQ4eK3za7Sv1d4r5S1dCklJ0Lw5VK7slSJVPqQJXSk/czgddP60M7c3vD3PZ4Wm0u4WBZrQlfK7rce28kvcL1xWzDsTraSkXEjovXp5pUiVT2lCV8qPRIS4M3E4nnZ4rXW+di38/TdUrw4NG3qlSJVPaUJXyo8m/jyRnp/3BC+exTlvnnXfq5eeHVrQaUJXyk9EhIFRAznw8AGvtc7h4oSuCjZN6Er5yWOLHqPTp52oVrqa18rcuxdiY6FkSbj+eq8Vq/IpPbFIKT9pENGA1jVae7XM1NZ5165QpIhXi1b5kLbQlfKDz2I/o3hocfrU7ePVcr/91rrv3durxap8ShO6Un4w8oeR7D3lnbNCU/3zj3Xt0JAQ6N7dq0WrfEq7XJTysf2n9hM7IpYqJat4tdwFC8DphPbtoWxZrxat8iltoSvlQw6ng8j/RbJkzxKvl53a3XLTTV4vWuVT2kJXyocKmULMHzif7ld6t08kKQl++MF6rP3nKpW20JXyEYfTQeHnC1O3fF2Ml8/4WbYMEhKgSROoWdOrRat8TBO6Uj5yJOEIbWu0JbJspNfL/uYb615b58qdx4RujKlujFlujNlqjNlijHkog23aGWNOG2M2uG7P+iZcpfIHh9PB7M2zWTxksVfPCgXrQGjq+HPtP1fusvNJSwYeFZF6QEvgfmNMvQy2WyUijV2357wapVL5zNxtc3ls8WMUDvH+Yapff4UjR6BWLZ2MS13MY0IXkcMist71+CywDajq68CUyq9EhBZVWhA/Jt7rrXOAr7+27m+6SSfjUhfL0afNGBMJNAEyuqrttcaYjcaYH4wx9b0RnFL50ZNLn6T2W7UpHlbc62WLXOg/7+Pdk05VEDAikr0NjSkBrABeFJGv0q0rBaSISLwxpjvwPxG5MoMyhgHDACIiIqJnzZqV1/gvEh8fT4kSJbxaZjDR/eOZN/ZR/HmrZV4stJiXorpgz57i3HVXc8qUOc+cOT8TEuL1KrKknyHPfL2P2rdvv05EmmW4UkQ83oBQYCHwSDa33weUz2qb6Oho8bbly5d7vcxgovvHs7zuowmrJsjY5WO9EktGxo0TAZG77vJZFVnSz5Bnvt5HwFrJJK9mZ5SLAT4CtonI65lsU8m1HcaYFlhdOSdy+p9Hqfzu90O/U7pIaZ+Vn9p/fvPNPqtC5WPZOQTfChgCxBpjNriWPQnUABCR94C+wAhjTDLwLzDA9Z9EqQLjj8N/ML7deKIqRvmk/N27YeNGa+7zjh19UoXK5zwmdBH5CQ8XzBKRycBkbwWlVH4jIjSd0pTJ3Sb7LKGnts579tS5z1XGdC4XpbwgOSWZ2BGxPkvmAF+5hiLo6BaVGT31X6k8cjgdhL0QRuL5RJ/VcfAg/PILhIdDt24+q0blc5rQlcqjREcio64bRbOqGY8k84bU7pYuXUBHDarMaJeLUnngcDq4d/69TOk5xSdnhaZK7W655RafVaGCgLbQlcqDNYfWMHvLbEoU8V2z+dgxWLECQkPhxht9Vo0KAprQlcolEQEB5zNOn7bOv/0WUlKsoYplyvisGhUENKErlUsvrHyBVh+38vrFK9KbM8e679vXp9WoIKAJXalcGhg1kF0P7vJpQv/nH1i6FEJCdO5z5ZkeFFUqF0YtGsWGIxtYPGSxT+uZNw+Sk+GGG6BcOZ9WpYKAJnSlciGiRAS3R9zu83q+/NK619EtKjs0oSuVQwv+XEDDiIZ0rt3Zp/WcOgWLF0OhQnp2qMoe7UNXKod6zOxB7JFYn9fz7bfgcEC7dlCxos+rU0FAW+hK5cCxhGMcfOQgVUpW8XldX3xh3d96q8+rUkFCW+hKZZPD6aDixIr8FpfRFRi9y727Rec+V9mlCV2pbBKET276hN5X9/Z5XandLddfr90tKvs0oSuVDQ6ng8hJkXSs1dGnZ4WmSu1u6d/f51WpIKIJXals2H96P0VCilCpZCWf13XyJCxapN0tKuc0oSvlgTPFyc8HfmbXyF1+aZ1//bV1MlGHDlChgs+rU0FEE7pSHkxZP4U7vrnD53O2pJo927rv188v1akgogldqSyICL2u6sXxUcf90jo/dsyau6VwYe1uUTmnCV2pLIxeMpqrJl9FuWL+mUjlq6/A6dS5W1Tu6IlFSmWhTY02dK3d1W/1zZpl3evoFpUb2kJXKhPvrHmHuDNxdLi8g1/qO3TIujJRWJhOlatyRxO6UpmY+sdUzpw747f6vvwSRKB7dyhd2m/VqiCiXS5KZWD78e3M6TeHyDKRfqvz88+t+4ED/ValCjLaQlcqHWeKk7pv12XhroV+q3PvXvjtNyheHHr29Fu1KshoC12pDKy+czXXVb/Ob/WlHgzt3RuKFfNbtSrIaAtdKTeCUPj5wpQu4t9O7NTulgED/FqtCjIeE7oxproxZrkxZqsxZosx5qEMtjHGmDeNMbuMMZuMMU19E65SvuVMcTKowSDqVqjrtzpjY63bZZdBly5+q1YFoex0uSQDj4rIemNMSWCdMWaxiGx126YbcKXrdg3wruteqXzD4XTwd/zffNDzA7+cFZoqtXV+663WkEWlcsvjp1ZEDovIetfjs8A2oGq6zXoDn4jlV6CMMaay16NVyoeW7l3KkYQjhIeG+63OlBSYOdN6rKNbVF7l6KCoMSYSaAKkv2RLVeCA2/M417LD6V4/DBgGEBERQUxMTM6i9SA+Pt7rZQYT3T8eJEOdknVYuWKl36qMjS3N/v1NqFAhCafzVwL9z6OfIc9s3Ucikq0bUAJYB9ycwbr5QGu350uBZlmVFx0dLd62fPlyr5cZTHT/ZO6ZZc8I4/D7Pho+XAREHn/cr9Xmmn6GPPP1PgLWSiZ5NVsdhcaYUGAu8JmIfJXBJgeB6m7Pq7mWKZUv3Hz1zWwesdmvdZ4/f+HKRLfd5teqVZDKzigXA3wEbBOR1zPZbB5wu2u0S0vgtIgczmRbpQLKM8ue4c3f36R+xfp+rXfhQvjnH4iKgoYN/Vq1ClLZ6UNvBQwBYo0xG1zLngRqAIjIe8ACoDuwC0gE/uP1SJXykQRHAi2qtvB7vTNmWPfaOlfe4jGhi8hPQJaXanH169zvraCU8pdV+1fRr34/WlZr6dd6T5+Gb78FYzShK+/RM0VVgSUitJ3Wlt/i0g/a8r25c+HcOWjXDqpX97i5Utmic7moAivBkcCekXuoVbaW3+v+9FPrfvBgv1etgpi20FWB5HA6KPlySfac3OP3uvfvh5gYCA+HW27xe/UqiGlCVwWSI8XB651fp32t9n6v+7PPrPvevfVCFsq7NKGrAsfhdNDpk04MaTjEr3O2gHVFok8+sR7ffrtfq1YFgCZ0VeBsO76NNYfWcFmxy/xe95o1sGMHVKwInTv7vXoV5DShqwJFRPjr9F+ce+qc31vnANOnW/eDBkFhHZKgvEwTuipQJv48kRs/v9HDmRW+ce7chalyhw71f/0q+GlCVwWGiDAwaiAHHj5gS+t8/nw4eRIaNbJuSnmbJnRVYDy66FE6fNKBaqWr2VJ/aneLts6Vr2gvniowGldqTNuabW2p+++/YcECq9980CBbQlAFgLbQVYEwY9MMwguHc9PVN9lT/wxwOqFHD2uEi1K+oAldFQgP//gwe0/utaVuEfj4Y+uxdrcoX9IuFxX09p/az6YRm6hSsoot9a9ZA1u3QoUKVgtdKV/RFroKag6ng8j/RbJkzxLbYkhtnQ8eDKGhtoWhCgBtoaugVsgU4vtB39Ptim621J+YCDNnWo/vvNOWEFQBoi10FbQcTgeFny/M1eWuxrqSov99/TWcOQMtWliXmlPKlzShq6B1JOEI19e8nsiykbbF8NFH1r22zpU/aEJXQcnhdDBr8ywWDV5ky1mhALt3w/LlULQoDBhgSwiqgNGEroLSV9u/YtTiURQOse8w0dSp1n2/fjrvufIPTegq6IgIzSs3J2FMgm2t8+TkC6Nb7rrLlhBUAaQJXQWdJ5c+Se23alMsrJhtMSxYAIcPw1VXQevWtoWhChgdtqiCTrcrunFz3ZttjeGDD6z7e+4BmwbYqAJIW+gqqEz4aQJL9i6hedXmtsUQF2e10END4Y47bAtDFUCa0FVQWXtoLWXDy9oaw9SpkJICffpYp/sr5S/a5aKCxh+H/2Bcu3FEVbTvDB6nEz780Hp8zz22haEKKG2hq6AgIjSd0pQV+1bYGsePP8KBA1C7NnToYGsoqgDy2EI3xkwFegJHReSSpo8xph3wLZA6N+lXIvKcF2NUyiNHioPYEbG2ts4B3n/fuh82DAppc0n5WXY+ctOArh62WSUijV03TebKrxxOB0VeKELC+QRb4zhwAL7/3joYqvOeKzt4TOgishL4xw+xKJUriY5EHr/ucVtHtoA1VDElBW6+Wa9KpOxhRMTzRsZEAvOz6HKZC8QBh4DHRGRLJuUMA4YBRERERM+aNSu3cWcoPj6eEiVKeLXMYBKM+0cQ9p7cS80yNQkxIXkuL7f7KDnZMGBAS06cKMIbb/xB48an8xxLIArGz5C3+XoftW/ffp2INMtwpYh4vAGRwOZM1pUCSrgedwf+zE6Z0dHR4m3Lly/3epnBJBj3z+q/VgvjEGeK0yvl5XYfffmlCIjUqyeSkuKVUAJSMH6GvM3X+whYK5nk1TwfthGRMyIS73q8AAg1xpTPa7lKeZL6IXY+47RtzpZU775r3Q8frmeGKvvk+VtgjKlkXFcPMMa0cJV5Iq/lKuXJCytfoPXHrW27eEWqbdtg2TIoVgxuv93WUFQBl51hi58D7YDyxpg4YCwQCiAi7wF9gRHGmGTgX2CA62eBUj41MGoggxoMsj2hp7bOBw/WaXKVvTwmdBEZ6GH9ZGCy1yJSKhtGLRrFH3//wZLb7bv4M0B8PEyfbj2+7z5bQ1FKzxRV+VNEiQjuaGT/zFeffmpdM7RVK2jUyO5oVEGnc7mofOf7nd/ToGIDulzRxdY4RGCy67fpgw/aGopSgLbQVT7U8/OebD662e4wWL4ctm6FypWtmRWVspu20FW+cjThKAcfOUiVklXsDoW33rLu770XwsLsjUUp0Ba6ykccTgcREyP4Ne5Xu0Nh716YN8+at+Xee+2ORimLJnSVbwjCjD4zuOnqm+wOhXfeseZt6d8fKlWyOxqlLJrQVb7gcDqo8UYN2ke2t/2s0ISECxexGDnS1lCUuogmdJUv7D+9n6KhRalU0v7m8CefwKlT0LIlNLd3gkelLqIJXQU8Z4qT1X+tZteDu2xvnaekwP/+Zz3+739tDUWpS2hCVwHvwz8+ZOi3Q20/xR9g4ULYsQOqV7fmPVcqkGhCVwFNROhxRQ+Ojzpue+sc4PXXrfsHHoDCOuhXBRj7vyFKZWH0ktFcOflKyhUrZ3cobNoES5ZA8eLWNUOVCjTaxlABrU2NNnS7opvdYQDwxhvW/V13QZkytoaiVIa0ha4C1ttr3ubAmQO0r9Xe7lA4fBhmzoRCheChh+yORqmMaUJXAWvahmnEn4+3OwwA3nwTzp+3DoRefrnd0SiVMe1yUQFp+/HtfHnrl0SWibQ7FM6ehffesx4/9pi9sSiVFW2hq4CTIinUfbsuC3cttDsUAD76yDqRqHVruOYau6NRKnPaQlcBR0T4+c6fubb6tXaHgsNxYaiits5VoNMWugooDqeDws8XplSRUnaHAsCsWXDgANStCzfeaHc0SmVNE7oKKKeSTjG44WDqVqhrdyikpMArr1iPR42yRrgoFcj0I6oChsPpYMJPE3i/x/sBcVboggWweTNUqQKDBtkdjVKe2f+tUcpl2d5lvP7r64SHhtsdCiLw8svW40cfhSJF7I1HqezQhK4CgohQpWQVHE87AqJ1vmoV/PwzXHaZnuav8g/7vzlKAWNjxtLwvYYUDgmMgVcvvmjdP/gglChhbyxKZZcmdBUQbql7C1tGbLE7DADWrIFFi6xErlckUvlJYDSHVIH2zLJnOHj2IFN7T7U7FABeesm6HzHC6nJRKr/QFrqyXaIjkWuqBsYpmLt3F+ebbyA8HB55xO5olMoZjwndGDPVGHPUGLM5k/XGGPOmMWaXMWaTMaap98NUwWrl/pX0rdeXe5vda3coAMyYUROwDoRWsv/ypUrlSHZa6NOArlms7wZc6boNA97Ne1iqIBARrp92Pb8f/N3uUADYtg1WrKhAWBg8/rjd0SiVcx770EVkpTEmMotNegOfiIgAvxpjyhhjKovIYW8FqYJTgiOBPSP3UKtsLbtDAeD550HEcOedULWq3dEolXPeOChaFTjg9jzOteyShG6MGYbViiciIoKYmBgvVH9BfHy818sMJoG0fwRh/eH1XHXZVewvst/ucNi/vxizZjWncGGhffvfiIk5Z3dIASmQPkOBys595NdRLiIyBZgC0KxZM2nXrp1Xy4+JicHbZQaTQNo/iY5ENqzdQI+WPQLiRKKBA62zQ7t3P0S/fvbP8hioAukzFKjs3Efe+CYdBKq7Pa/mWqZUhhxOBx0/6ciQhkMCIplv3gyzZ0NYGNx22192h6NUrnnj2zQPuN012qUlcFr7z1VWth/fzrpD67isWGAM8h43zmqdDxsGFStqV4vKvzx2uRhjPgfaAeWNMXHAWCAUQETeAxYA3YFdQCLwH18Fq/I/EWHfqX0kPZUUEK3zP/6AuXOtcedjxsDOnXZHpFTuZWeUy0AP6wW432sRqaD22i+vMWrxKJzPOu0OBYCnn7buR4ywpsnVhK7yM/ubSKrAEBEG1B9A3H/jAqJ1/vPP1pznJUpYrXOl8jv7v1WqwHhs0WO0/6Q9VUvZP8hbBJ580nr88MNQoYKt4SjlFTo5l/KbxpUa07ZmW7vDAODHH2HFCihb1rqAhVLBQFvoyi8+3fQpYYXD6H11b7tDISXlQhfLk09CmTK2hqOU12hCV37xyMJH2H/K/jNCAT7/HDZuhGrV4H49nK+CiHa5KJ/bd2ofG4dvpErJKnaHQlISPPWU9fi556BoUXvjUcqbtIWufMrhdFDrf7VYvHux3aEA8M47sH8/REXB7bfbHY1S3qUtdOVThUwhFgxaQNcrspqB2T/++QdeeMF6PGEChITYG49S3qYtdOUzDqeDws8Xpk65Ohhj7A6HF16AkyehY0fo3t3uaJTyPk3oymeOJhylXWQ7IstG2h0Ku3bB5MlgDEycaN0rFWw0oSufcDgdzIydycLbFgbEWaGjRoHDAXfcAY0b2x2NUr5h/zdNBaWvt3/N40sep3CI/Ydpli+Hb76B4sXhpZfsjkYp39GErrxORIiuHE3CmATbW+fJyfDQQ9bjMWOgcmVbw1HKpzShK697atlTXPHWFRQLK2Z3KEyZArGxEBkJjzxidzRK+Zb9v4dV0Olauys3X32z3WFw4gQ884z1+LXX9CQiFfy0ha686uVVL7N472KaVW1mdyg8+aQ19rxjR+jTx+5olPI9TejKq/74+w8uC7f/0nJr18IHH0DhwvDWWzpMURUM2uWivGb94fU80/YZGkQ0sDUOp9O6ApGINdd53bq2hqOU32gLXXmFiBA9JZoV+1fYHQpTplgt9GrVYOxYu6NRyn+0ha68wpHiIHZELFEVo2yN4++/L8x1/r//WZeXU6qg0Ba6yjOH00GRF4qQcD7B7lB4+GE4fdqaq0UPhKqCRhO6yrNERyJPtHqC5lWb2xrHDz/A7NlQrBi8/bYeCFUFj3a5qDxxOB3c8909fHDjB7aeFXr2LNx7r/V4/HjrRCKlChptoas8WXtoLV9u/ZKSRUraGseTT8KBAxAdbXW7KFUQaUJXuSYiOFOcOJ9x2to6X7XKmho3JAQ+/NAae65UQaQJXeXaCytfoM20NrZevCIxEe6803o8ZoxOjasKNk3oKtcGNRjErgd32ZrQn3rKunhF/frw9NO2haFUQMhWQjfGdDXG7DDG7DLGPJHB+qHGmGPGmA2u293eD1UFklGLRnHPd/dQ+7LatsWwYoU11jwkBKZNgyJFbAtFqYDgsbfRGBMCvA3cAMQBa4wx80Rka7pNZ4vIAz6IUQWgyiUrc2elO22r/8wZGDrUOr3/qaegmf1zgSllu+wcPmoB7BKRPQDGmFlAbyB9QlcFxPyd86lXoR5dr+hqWwwPPQT79kHTplZCV0plr8ulKnDA7Xmca1l6txhjNhlj5hhjqnslOhWQbvz8RrYc3WJb/XPmWF0s4eEwYwaEhdkWilIBxYhI1hsY0xfoKiJ3u54PAa5x714xxpQD4kXknDHmXqC/iHTIoKxhwDCAiIiI6FmzZnnvnQDx8fGU0Mk7MuWN/ZOckowghBYK9VJUOXP0aBHuuqsZ8fGhjBz5J336HPRq+foZypruH898vY/at2+/TkQy7mQUkSxvwLXAQrfnY4AxWWwfApz2VG50dLR42/Lly71eZjDJ6/45n3xeGIfM2TLHOwHlkMMh0ratCIj06CGSkuL9OvQzlDXdP575eh8BayWTvJqdLpc1wJXGmFrGmDBgADDPfQNjjPuld3sB23L0L0flC4Iwo88M+tS1Z9ar556DlSuhUiWYOlXnalEqPY8HRUUk2RjzALAQq/U9VUS2GGOew/pPMQ8YaYzpBSQD/wBDfRizsoHD6aDa69X4494/bDkrdMkSeOEFK4l/9hlUrOj3EJQKeNk6SVpEFgAL0i171u3xGKyuGBWk/jr9FyWLlKRyycqeN/aygwdh0CBriOKzz0KHS47OKKVAzxRV2eBMcbJy/0p23L/D763z8+ehXz84dgw6dbISulIqY5rQlUcf/vEhd867k0KF/P9xefRR+Pln63Jyn31mnRWqlMqYJnSVJRGhxxU9OD7quN9b5x9/bM2iGBZmjT3XfnOlsqYJXWVp9JLRXDn5SsoVK+fXen/7DYYPtx5PngzXXOPX6pXKl3TmaJWlNjXa0P2K7n6t86+/oHdvq//8vvvgnnv8Wr1S+Za20FWm3v79bf46/RftarXzW51nz0KvXnDkCHTsCJMm+a1qpfI9TegqU59s+oQER4Lf6nM4rBEtGzfClVfCl19CqD0zDCiVL2mXi8rQ9uPbmXXLLGqVreWX+kRgxAj48UcoXx5++AHKlvVL1UoFDW2hq0ukSAp1367Lwt0L/VbnM8/ARx9B0aIwbx7Utu+6GUrlW9pCV5cQEX656xdaVmvpl/omTYIXX7TGmH/xBVx7rV+qVSroaAtdXcThdFD4+cKUCPXPFKkffQT//a/1+MMPoWdPv1SrVFDShK4ucvrcaYY0HEK9ivV8XteMGReGJE6aZF1STimVe5rQVRqH08GLK1/kvR7v+fys0E8/hTvusA6GvvyydUk5pVTeaEJXaZbtXcak3yYRHhru03o++shK5ikp8Pzz8MQTPq1OqQJDE7oCrAOhlUtUxvG0w6et8//9D+6+22qZv/QSPP20z6pSqsDRhK4AGBszlkbvN6JwiG8GPonAU0/Bww9bzydNgjE6g75SXqXDFhUAt9S9hQH1B/ik7PPnrVb5p59aQxNTu1yUUt6lCV3x9LKniTsTx7Sbpnm97OPHoW9fWLECihe3xpl39+9cX0oVGJrQFUnJSVxbzftn82zaBDfdBHv3QuXKMH8+NG3q9WqUUi6a0Au4lftXcnPdm7mu+nVeLXfGDBg2DP79F6Kj4dtvoWpVr1ahlEpHD4oWYCLC9dOu5/eDv3utzPh4uOsuGDLESuZDh8KqVZrMlfIHbaEXYPHn49n70F4iy0R6pbzffoPBg2HXLggPh7fespK7MV4pXinlgbbQCyiH00GpCaX488SfeS4rMREefxyuu85K5g0awJo11sgWTeZK+Y8m9ALKkeLgjS5v0PHyjnkqZ/58iIqCV1+1nj/+OPz+u7VMKeVf2uVSADmcDtpPb8/8gfNzfVZobKyVvH/80XresCFMmaIXc1bKTtpCL4C2H9/Oxr83Uq5YuZy/djvcdhs0amQl81Kl4PXXYe1aTeZK2U1b6AWMiLDv1D4Sn0zMdutcxBqpMmkSfPON9Tw0FIYPt640VKGCT0NWSmWTJvQC5rVfXmPU4lE4n3V63PbgQZg1C6ZOha1brWVhYfCf/1jzsNSs6eNglVI5kq0mmjGmqzFmhzFmlzHmkslOjTFFjDGzXet/M8ZEej1SlXuffQaRkbBuHQPumkRczTczbJ07nbBuHUyYAK1bQ/Xq8NhjVjKvWNFqje/bB++9p8lcqUDksYVujAkB3gZuAOKANcaYeSKy1W2zu4CTInKFMWYA8H9Af18ErHLos89g2DCSE8+xq0hhhrZN4KcRb7Lp8OUcbtqDPXtgxw7YuNHqB4+Pv/DSIkWgRw9rbHnPnlY3i1IqcGWny6UFsEtE9gAYY2YBvQH3hN4bGOd6PAeYbIwxIiJejFXlxlNPQWIiY3mBlx58CHiI6gBPZrz55ZdDhw7QpYt1K1nSj7EqpfIkOwm9KnDA7XkckH48Q9o2IpJsjDkNlAOOu29kjBkGDAOIiIggJiYmd1FnIj4+3utl5nsPPgjA30uuocjyZAqbZMLDkilRNIlyVUOoWDGJ6tX/pVateOrUieeyy86nvXTdOruCto9+hrKm+8czO/eRXw+KisgUYApAs2bNpF27dl4tPyYmBm+Xme8NHQr799MOGDJxIu0eewySgLI1Yd0+W0MLRPoZypruH8/s3EfZOSh6EKxf6S7VXMsy3MYYUxgoDZzwRoAqj158EYoVu3hZsWLWcqVUUMlOQl8DXGmMqWWMCQMGAPPSbTMPSL0GTV9gmfafB4jbbrNO4UwdllKzpvX8ttvsjUsp5XUeu1xcfeIPAAuBEGCqiGwxxjwHrBWRecBHwKfGmF3AP1hJXwWK226zbjEx1rhDpVRQylYfuogsABakW/as2+Mk4FbvhqaUUiondC4XpZQKEprQlVIqSGhCV0qpIKEJXSmlgoQmdKWUChKa0JVSKkhoQldKqSChCV0ppYKEJnSllAoSxq4pV4wxx4D9Xi62POmm7FUX0f3jme6jrOn+8czX+6imiGR4JV/bErovGGPWikgzu+MIVLp/PNN9lDXdP57ZuY+0y0UppYKEJnSllAoSwZbQp9gdQIDT/eOZ7qOs6f7xzLZ9FFR96EopVZAFWwtdKaUKrKBL6MaYW40xW4wxKcYYPRrvYozpaozZYYzZZYx5wu54Ao0xZqox5qgxZrPdsQQiY0x1Y8xyY8xW1/frIbtjCjTGmHBjzO/GmI2ufTTe3zEEXUIHNgM3AyvtDiRQGGNCgLeBbkA9YKAxpp69UQWcaUBXu4MIYMnAoyJSD2gJ3K+foUucAzqISCOgMdDVGNPSnwEEXUIXkW0issPuOAJMC2CXiOwRkfPALKC3zTEFFBFZiXU9XJUBETksIutdj88C24Cq9kYVWMQS73oa6rr59SBl0CV0laGqwAG353Hol1HlkjEmEmgC/GZzKAHHGBNijNkAHAUWi4hf91G2LhIdaIwxS4BKGax6SkS+9Xc8ShUUxpgSwFzgYRE5Y3c8gUZEnEBjY0wZ4GtjTJSI+O24TL5M6CLSye4Y8pmDQHW359Vcy5TKNmNMKFYy/0xEvrI7nkAmIqeMMcuxjsv4LaFrl0vBsAa40hhTyxgTBgwA5tkck8pHjDEG+AjYJiKv2x1PIDLGVHC1zDHGFAVuALb7M4agS+jGmD7GmDjgWuB7Y8xCu2Oym4gkAw8AC7EOZn0hIlvsjSqwGGM+B34B6hhj4owxd9kdU4BpBQwBOhhjNrhu3e0OKsBUBpYbYzZhNaIWi8h8fwagZ4oqpVSQCLoWulJKFVSa0JVSKkhoQldKqSChCV0ppYKEJnSllAoSmtCVUipIaEJXSqkgoQldKaWCxP8DiWHf2rDEIOkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#########################\n",
    "###### Solution 1.1 #####\n",
    "#########################\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(0, 2, 100)  \n",
    "\n",
    "# Parametric equations\n",
    "x = t\n",
    "y = t**2\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(x, y, label='Curve: α(t) = (t, t^2)', color='blue', linewidth=2)\n",
    "plt.scatter([0, 2], [0, 4], color='red', marker='o', label='Endpoints')\n",
    "plt.arrow(0, 0, 2, 4, head_width=0.1, head_length=0.1, fc='green', ec='green',linestyle=\"dotted\", label='Direction of Traversal')\n",
    "plt.title('Solution 1.1: Parametric Curve α(t) = (t, t^2)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal')  # Equal scaling for x and y axes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cf220ee0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###################################\n",
    "###### Solution 1.2  ##############\n",
    "###################################\n",
    "\n",
    "\n",
    "# parameter range between 0 and 6π\n",
    "t = np.linspace(0, 6 * np.pi, 100)\n",
    "\n",
    "# Parametric equations\n",
    "x = t * np.cos(t)\n",
    "y = t * np.sin(t)\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.plot(x, y, label='Curve: α(t) = (t cos t, t sin t)', color='blue', linewidth=2)\n",
    "plt.scatter([0, 6 * np.pi], [0, 0], color='red', marker='o', label='Endpoints')\n",
    "plt.arrow(0, 0, 20, 20, head_width=0.1, head_length=0.1,color=\"green\",linestyle=\"dotted\", label='Direction of Traversal')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Solution 1.2: Parametric Curve α(t) = (t cos t, t sin t)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8ecc804f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X25cnf3uSJpFN6HV5L2vDCZdTnuvfWHn89q233pp3/5ZbbmHWrFmMGjWKWbNmMWvWLLZs2cL69eu57rrr8PLy4vz581SvXh2gwC+G/P7880+GDjUujNS7d28WLFhAgwYNAEhNTSUy0v7AhQDe3t74+fnZ/UwWL15c6veVmppKo0bGdcMzMzNZtmwZN998c978M2cce/3sP/74g+TkZNq0aQPAqVOnimyN23Py5El27NhBjRo1yrztmjVrsnbtWq6++uq856pVq8b+/fvLvK7CXL7A53bR5HZhRQdFc+ipQ/xz4B9G/z6a165+zbpwQpRCkyZNmD17tt15Pj4+5ORcuI504eOg8w9de+utt3LzzTdzww03oJSiXr16rFu3jiZNmvDbb7+V6UuoUiXjmt3BwcG0bNky7/mAgIASj8U+c+YM/v7+Fz3fqVMnMjIyLnr+v//9b4HiVng7OTk5hIWFsXr16lLnLyutNffeey+vvVb2erFixQquueYaevbsSXR0dN7zzz33HHPnzgUoNvuwYcO49tprGT16NM8//zxg/DsHBASUOUthLt8Hn78FnysyMJIWUS14Y+kbrDu4zppgQpTSVVddxZkzZ/jkk0/ynlu7di2LFy8mLi6OjRs3cubMGY4dO8Yff/xR5Hrq1q2Lt7c3L7/8cl7LvkGDBqSlpbFixQrAGJZhw4YNxeZp3bp13g6+2bNnF9gx2KhRI7Zv35732NfXt8AOwiNHjhAREWH3dPrFixezevXqi6bCxb3wdkJCQqhTpw5ff/01YBTjNWvWFPsecgUHBxf4Utm3bx/du3e/aLnu3bsze/ZsDh0yrpF+9OhRdu3aVapttGvXjv3797N8+fK8vnWAV199Ne892suSa9y4cSxYsCCvuANs3bqVpk2blmr7xXH5Al+4BZ8rKiiKU8+dYtHuRQz7eVjFBxOilJRSfPfdd/z+++/UrVuXJk2aMHr0aKKjo4mJieGWW26hadOm3HLLLQVa0/bceuutfPHFF9xyyy2AcWTL7NmzeeGFF2jRogXx8fEsW7YMgI8++oiPPvroonUMGzaM5cuXc+2113L69Gl69erFkCFDAOjbty9JSUl5yw4cOJDmzZvn7WRNTEykb9++l/yZ9OnTh0WLFuU9nj59OpMmTaJFixY0adKEH374oVTrad68Od7e3rRo0YJ33nmH1NTUvB23+TVu3JhXXnmFnj170rx5c3r06FHizuj8KlWqRFxcHOnp6UUuc9tttzF+/HhatmxZ4IsgPT2devXqFVjWUZ+j5TtW80/l2cl6+rSxE8vPz/7yu4/t1nHvxOl9x/eVuG5HcYWdl1q7Rs6K3slaHsXteHMWjsqYlZWl27Vrp7Ozs+3Ov/766/WWLVvKte7CGQcMGJC3Y9VRJkyYoH/44Ydyv764z7FPnz567ty5ZVrfmTNndHh4uD558mSB5zt16qSPHj160fJl3cnqNi34s2ft7yCLCY3h3+H/Mm7JOAb9NKhiwwnhZgICAhg7diz79u27aN7Zs2cZMGAA9evXd8i2Xn/99TK1oktjyJAh9O/f36HrzPXII48wZsyYIk90KiwxMZHWrVtz3333Ubly5bzn09LSeOKJJwgPD7/kTC6/k9XLy5hycuD8ebDz6wulFEPbDuWp+U9xMPMgUUFRFR9UCDfRq5f9o9P8/Py4x4HjhTRo0CDv6B1X0L9//zJ9eeSe6FRYZGQkAwYMcEgml2/Bg/0drYU1iGjAT7f/xM1f38zQeUMrJpgQQljILQp8UTta7fm0/6eEVAph25Ft5oYSQgiLmVbglVINlFKr800nlFIjzNhWbgu+NAW+ftX6vHzVy3Sc3JFn5j9jRhwhhHAKphV4rfUWrXW81joeSACygO/M2Fb+Ha2l4aW8+Pvhv2ke1ZyFKQvNiCREmXh7exMfH0+TJk1o0aIFb731Vt4JTitXrmTYMMcc6pt/cDCADh06OGS9Rdm8eTPx8fEXHRrYrl074uPjiY2NJTIykvj4eDp27EhKSoqpecrjvvvuK/JENGdXUTtZuwM7tNalO3OgjMrSRZMrLiyOyMBIAscF8nr313nmSmnNC0NSShKj/xhNsF8wHWI68NafbzGw1UCOnDpCUkoS98Xfx09bf6JGUA0SaiTw2uLXeKL9E6QcS2FV6ipub3Y732z6hvpV6tMsqhljF45Fv1D8GAgBAQF5J8QcOnSIO+64gxMnTjB27Fhat25N69atL3pNdna23WO6izNu3DieffbZvMe5x8Sb5fvvv+emm25izJgxBZ7PPfFq6tSprFy5kokTJxYY3qA87600zFqvs6qoPvjbgC/NWnlpdrLaU9m3MrtG7KJjbEemr3XAyG3CLdzxzR0s37uc+TvnM3bhWDLPZvL28reZtmYau47vYuzCsaxKXcWcbXMYu3AsZ3PO8vrS15m5YSZbj25l7MKxrD+0nm83f8vYhWN5ocsLZdp+tWrV+OSTT5g4cSJa6wIjSr744ovcfffddOzYkbvvvpu0tDRuvPFG2rRpQ5s2bfLOQM3MzOT++++nWbNmNG/enB9++MHu6I9BQUGAcT7MyJEjadq0Kc2aNcsb8jcpKYmuXbty00030bBhQ+688060neORV69ezRVXXEHz5s25/vrrSU9PZ968ebz77rt8+OGHdOvWrcT3PW7cuALvLSUlhU6dOtGqVStatWqV92V022235Q0BABda2OfPn2fkyJG0adOG5s2b8/HHH+e9h06dOtG/f38aN27MyZMn6du3Ly1atKBp06Z57/Wll16iTZs2NG3alIEDB9p9n67G9K8ypZQf0B8YXcT8gcBAgKioqAJnydmTmZl50TLnzrUBAlm69C/27csqc8bsnGwOHDzAN/u+oWpA1TK/vjQZnZEr5KyIjKGhoQVOIe9VuxdT10912PpX7Vtl9xT1wvIvExkZyfnz59m5cydZWVlkZ2eTkZHBmTNnWL9+Pb/++isBAQE88MADDBo0iPbt27Nnzx6uv/56Vq5cyfPPP09AQEBeUTxy5AjXXXcdEydOzBv0K3d7GRkZ/PDDDyQnJ7NkyRKOHDlC165dadWqFVlZWfzzzz+sWLGC6tWr06NHD+bPn0/79u0LZL/rrrsYP348V155Ja+88grPPfccb7zxBvfffz9BQUEMGzbM7mdw+vRpzp49S0ZGBlrrAu8tKyuLb7/9Fn9/f7Zv386DDz7IwoUL6d+/P9OnT6dz586cPXuW33//nTfffJMPPvgAf39/FixYwJkzZ+jZsycdOnQgKyuLVatWsXz5cmrXrs13331HZGQkM2fOBOD48eNkZGRw77335l184+GHH+brr7+mT58+nDt3jlOnTpGRkcH58+dL9W9pltOnT5fp/0NF/FbpA6zSWtu9eoHW+hPgE4DWrVvrrl27Fruy3BZFfmFhsHs3tGzZlhYtyheywfEGHMg8wMJdC3mqw1PlW0kxGZ2RK+SsiIybNm0qMBBXUECQQ9f/74l/SzXQl71lgoKCqFy5Mj4+PgQHB1OpUiUGDBiQN9LhwoUL2bbtwhFhmZmZKKVYtGgRM2fOLLDO3PuFtxMcHExycjJ33XUXYWFhhIWF0bVrVzZt2kRISAht27alYcOGACQkJHDo0KEC6zh+/DgnTpygT58+gDF8wc0335yXt1KlSkW+f39/f/z8/AgODkYpVeC95eTkMGTIEFavXo23tzdbt24lODiYG264gVGjRuHn58eCBQvo0qUL1apVY9GiRaxdu5affvopL1dqaiqVK1embdu2eePjt23bljFjxvDKK6/Qr18/OnXqBMBvv/3Gm2++SVZWFkePHiU+Pp7g4GB8fX0JCAjIG0vGqpFDwfi8ShquIr+KKPC3Y2L3DJR9J6s9MaEx+Hn7MXL+SJpXa07Py3s6JpxwOTPWO/bKYDc2urHMr9m5cyfe3t5Uq1aNTZs2FZiXfwTJnJwcli9fbnf0RkfJHVkSjJ3Bjroknz3539s777xDVFQUa9asIScnJ+89+vv707VrV3799VdmzZrFbbfdBhjdTBMmTLjoRKykpKQC661fvz6rVq1i3rx5jBkzhu7du/P000/z2GOPsXLlSmJiYnjxxRdLHDXTFZjaB6+UCgR6AN+auZ3y7GS1JyooirSRaeSQw6jfR116MOGShrZ17IlwX64rW/smLS2NRx55hCFDhqBKuBxUz549mTBhQt7j3B21PXr04IMPPsh7PncQrMKjP+bq1KkTs2bN4vz586SlpbFo0aICV4gqTmhoKOHh4XldP59//jldunQp1WuLc/z4capXr46Xlxeff/55gcsS3nrrrUyZMoXFixfnXb+0V69efPjhh3nvb+vWrZw8efKi9e7fv5/KlStz1113MXLkSFatWpVXzCMiIsjMzHTZo2YKM7XAa61Paq2raq2Pm7md8u5ktSeicgTx0fGMXzaeDYeKH1ZVuKeklCSHrq9V9VYlLpO787NJkyZcffXV9OzZkxdeKHnn7Pvvv8/KlStp3rw5jRs3zhsdcsyYMaSnp9O0aVNatGiRV3wLj/6Y6/rrr6d58+a0aNGCq666ijfffLPA2OYlmTZtGiNHjqR58+asXr26wNC35fXYY48xbdo0WrRowebNmwu0wnv27MnChQu5+uqr8bMVgIceeojGjRvTqlUrmjZtyqBBg+z+2li3bl3epfnGjh3LmDFjCAsL4+GHH6Zp06b06tUr78Ifrk45057i1q1b65UrVxa7jL0+2auvhj/+gN9+gx49HJPlTPYZPk7+mO1Ht/N+n/fL9FpX6NsG18hZUX3wuVcPAlBjFV3iutC1dlcm/DWBO5rewZnzZ5izdQ4DEwby645fCxxCeW/Te8k8n2n/EMolr/Hdrd9xTb1rTH0PJbG677g0JGPJCv+tAiilkrXWFx9HixsMNgaObcHnquRTiQENB9B1aldGXzma6sHVHbdy4dTyH7P+YtcXL5qf/7kXu7540X/6wvOFsIpbFHhH9cEXFhsay45hO3hs7mPk6Bw+vvZjx25ACCFM5BaDjZVlLJqyUkox/IrhpGWlcSDjgOM3IIQQJnGLAu+IwySL0zCiId/e+i03fn2jDDXsppxpX5QQ9pTnb9StCrwZLfj8pl43lfCAcLYc3mLuhkSF8vf358iRI1LkhdPSWnPkyJEyn+/gFn3wZuxktade1Xq82PVFqo2vxkOtHuL1q183d4OiQtSqVYu9e/eSlpZWrtefPn3a1BONHEEyOoaVGf39/alVq1aZXuMWBb6iWvBgDDWcPDCZZXuXkfhvIt3qlDyIknBuvr6+1KlTp9yvT0pKKtPp41aQjI7hChnzc4suGjN3stoTFxZH//r9ueqzqxi/dHzFbFQIIcrILQq82TtZ7Qn0C8wbavizNZ9V3IaFEKKUpIvmEsSGxhLgE0DHyR0BuKeF464oL4QQl8otWvAVtZPVnsjASPY8vodGEY14c+mbFR9ACCGKIC14B6gVUgtfL1+e+f0ZWkW3wsc9PlYhhIuTFryDRAVFcXjkYc7mnGVfxj7rggghhI1bFHirW/C5qlauSqvqrTiYeZBNaZtKfoEQQpjILQp8RR8mWZzooGhaVm/JL9t/Yci8IVbHEUJ4MLco8FYcJlkcheKGRjfw645fSc1ItTqOEMJDucXeQGfposkvLiyOrUO2MmjOIBRKhhoWQlQ4t2jBO8NOVnuUUjzR/gmOnjoqQw0LISqcWxT43Iu+nzljbQ57GkY05Otbvua6Wdcx7OdhVscRQngQKfAV5Ivrv6BKQBU5ukYIUWGkwFeQelXr8XyX5+k4uSOjfx9tdRwhhAeQAl+BvJQX/wz6h1bVW/H7jt+tjiOEcHNS4CtYXFgcfer1occXPfjvsv9aHUcI4cakwFsgyC/IGGo4piPTVk+zOo4Qwk25xXHwrlbg4cJQwx0md8Dby5u7mt9ldSQhhJtxqxb86dPW5iir3KGG61etzxtL3rA6jhDCzbhVgXelFnyuWiG1iA2NZdQfo0j8N9HqOEIINyIF3glEB0Vz5OkjnDx3kqfnP211HCGEm5AC7ySqBFShdY3WvLfiPbYc3mJ1HCGEG5AC70Sig6LJHJ3JT1t/kqGGhRCXzC0KvK8vKAXnzxuTK/P19uXmxjfz+87fZYAyIcQlMbXAK6XClFKzlVKblVKblFLtzdmO+7TiwTgZatPgTTy74FkemfOI1XGEEC7K7Bb8e8AvWuuGQAvAtJG23KnAgzHU8MgOIzl++rhcNEQIUS6mFXilVCjQGZgEoLU+q7U+Ztb23K3AAzSKbMSXN31J/y/7M/zn4VbHEUK4GDNb8HWANGCKUuofpdSnSqlAszbmjgU+15c3fUlkYCQb0zZaHUUI4UKU1tqcFSvVGlgOdNRar1BKvQec0Fr/p9ByA4GBAFFRUQkzZ84sdr2ZmZkEBQVd9Pxdd7Vl377KfPbZCmJiTjnqbZRLURkv1eoDq4kMjKRmcE2HrM+snI4kGR1DMjqGM2bs1q1bsta6td2ZWmtTJiAaSMn3uBMwt7jXJCQk6JIkJibafb5JE61B67VrS1yF6YrKeKl2HdulZ2+YrX/d9qtD1mdWTkeSjI4hGR3DGTMCK3URNdW0Lhqt9QFgj1Kqge2p7oBpfQzu3EWTKzY0lp51e9Jrei/e/vNtq+MIIZyc2UfRDAWmK6XWAvHAOLM25AkFHiC4UjApw1PoENOByf9MtjqOEMKJmTpcsNZ6NWC/b8jBPKXAg3GcfIBvAO0ntcffx587mt1hdSQhhBNyizNZwbMKPEC1wGrsfXwvdcPr8tri16yOI4RwQm5X4F1tTPhLUTOkJrXDavPsgmdJ+jfJ6jhCCCfjdgXeU1rwuaKCojj69FFOnD3ByPkjrY4jhHAiUuDdQHhAOG1rtmXCiglsPbzV6jhCCCchBd5NRAdFkzE6g+82fydDDQshACnwbsXX25dbmtxCUkoSBzMPWh1HCGExUw+TrEhS4A11wuuw/rH13Pv9vfh7+/PxtR9bHUkIYRG3acH7+xu3nl7gc42+cjQnz51k/4n9VkcRQljEbQq8tOALahjRkC9u+IJ+X/ZjxC8jrI4jhLCAFHg399XNXxEVFMX6Q+utjiKEqGBuU+Bzu2hOWTtSsNO5vMrlPN3hadpPas+YBWOsjiOEqEBuU+ADAoxbKfAX8/byZv2j62ldozW/bPvF6jhCiAoiBd5DxIXFcVWdq+gzow/vLn/X6jhCiArgNodJVq5s3EqBL1pIpRB2jdhFakYqk1ZNoi51rY4khDCRtOA9TGxoLHXC6/DQTw+Rfjrd6jhCCBNJgfdAuUMN+3n78eqiV62OI4QwiRR4D1UzpCaVvCsxJnEMi3cttjqOEMIEUuA9mI+XD+nPpJOWlcaTvz1pdRwhhIO5XYHPyrI2h6sJ8w+jfa32fPj3h2w/st3qOEIIB3K7Ai8t+LKrHlydE6NP8NXGrxg8d7DVcYQQDiIFXgBGd83tTW9n6Z6lMtSwEG7CbY6DlwJ/6eqE12H1I6u569u7CPQNlKGGhXBxbtmC19raLK5uTOcxnD5/WoYaFsLFuU2B9/YGX1/jvowoeWkaRjRk2oBp9J7em8d/edzqOEKIcnKbAg8yXIGjfXfrd9QIrsHag2utjiKEKAe3KvDSD+9YdavU5fH2j9NhUgf+s+A/VscRQpSRFHhRLB8vHzYO3kjbmm2Zt3We1XGEEGUgBV6UKDY0ls5xnen7ZV/eW/6e1XGEEKUkBV6USqh/KLtG7KJ9THs+Tf7U6jhCiFJwm+PgQYYrMFtsaCyVvCvR7tN2hPqHcnOTm62OJIQohrTgRZlEBUWx9/G91AqpxcsLX7Y6jhCiGFLgRZnVDKnJZeGX8XzS8yzdvdTqOEKIIpha4JVSKUqpdUqp1UqplWZuC6TAV6SooCiOPXOM1MxUGWpYCCdVES34blrreK11a7M3JAW+YoX6h9IxpiOfJH/CjqM7rI4jhChEumjEJakeXJ30Z9KZsX4Gj819zOo4Qoh8zC7wGvhNKZWslBpo8rZkqAKL+Hj5cGezO1mxd4UMNSyEE1HaxKEXlVI1tdb7lFLVgPnAUK31okLLDAQGAkRFRSXMnDmz2HVmZmYSFBRkd97kybX5/PPa3Hffv9x77y6HvIfyKC6jMzEj57/p/+Lt5U1saKxD1ucKn6VkdAzJWD7dunVLLrILXGtdIRPwIvBUccskJCTokiQmJhY57403tAatn3qqxNWYqriMzsSMnBsPbdQP/PCA3nt8r0PW5wqfpWR0DMlYPsBKXURNNa2LRikVqJQKzr0P9ATWm7U9gMBA4/bkSTO3IorTKLIRk/pPoucXPWWoYSEsZmYffBSwRCm1BvgLmKu1/sXE7ZH7yykz08ytiNL46fafiAmNYfWB1VZHEcJjmTZUgdZ6J9DCrPXbk9uClwJvvcvCL2NYu2GEvBbCUx2e4qVuL1kdSQiP41aHSea24KWLxjn4ePmwechm2tVsx5ytc6yOI4THccsCLy145xEbGkvH2I5c++W1TPxrotVxhPAoblXgZSercwrzD2PXiF20q9mOT1Z+YnUcITyGWw0XLC1455U71HDbT9tSpXIVbmp8k9WRhHB70oIXFSYqKIp9T+yjRnANXlooO12FMJu04EWFqhFcA2/lTcekjvS4rAftY9pbHUkIt+W2LXgTR2AQlygqKIrjo46z6/guGWpYCBO5VYH39gZ/f6O4y4Bjzi2kUgid4zrzv+T/8W/6v1bHEcItuVWBBzkW3pXUCK5B+jPpTF0zVYYaFsIEblfg5WxW1+Lt5c09ze8hOTVZhhoWwsHcrsDLjlbXU7dKXVY8tIKhPw/lkTmPWB1HCLfhdgVeDpV0XS91e4kcncPe43utjiKEW3C7Ai8teNfVMKIhH/f7mKs/v5onfn3C6jhCuDy3K/DSgndtSinm3TmP2NBYVqWusjqOEC7N7Qq8tOBd32XhlzG4zWDaT2rP/oz9VscRwmW5bYGXFrxr8/X2ZdvQbQT5BfHD5h+sjiOES3K7Ai+HSbqP2NBYAv0CGTBrAB/89YHVcYRwOW5X4KUF7168lbcx1HCtdnz090dWxxHCpbjVYGNwocBnZFibQzhO7lDDbf7XhsjASG5sfKPVkYRwCW7Xgg8JMW5PnLA2h3CsqKAo9j+xn6igKMYmjbU6jhAuwe1a8KGhxu3x49bmEI5XPbg6Sik6TelEn8v70LZWW6sjCeHUpAUvXEp0UDQnRp1gW/o2ORlKiBK4XYGXFrz7C64UTLfa3Ziyegop6SlWxxHCabldgc9twUuBd281gmtweORhJv0ziUfnPGp1HCGcktsV+NwWvHTRuD9vL2/ui7+PNQfXcCjzkNVxhHA6blvgpQXvGepWqcuyB5fxyNxH5KIhQhTidgU+ONi4PXFCrsvqSV696lW01uw+ttvqKEI4Dbcr8D4+xnAFWstwBZ6kUWQj/q/v/3HVZ1fx5K9yIW8hwA0LPMihkp5KKcX8u+dTJ7wOK/evtDqOEJZzywIv/fCeq054HQYmDKTj5I68mPSi1XGEsJRbFnhpwXs2P28/tg3dRoeYDny36Tur4whhGbcs8NKCF7GhsbSp0YYbvrqBD//+0Oo4QljCLQu8nOwkAMIDwtk1YhdtaraRIi88kumDjSmlvIGVwD6tdT+ztwdyspO4IP9Qw9WDqzOg4QCrIwlRYSqiBT8c2FQB28kjLXiRX1RQFKlPplI1oCovJL5gdRwhKoypBV4pVQvoC3xq5nYKkxa8KCw6KJr6Vevz0qKX+GvfX1bHEaJCKG3i6Z5KqdnAa0Aw8JS9Lhql1EBgIEBUVFTCzJkzi11nZmYmQbmXbSrCV1/V4sMPL+fGG/cyZMj28sYvt9JkdAaukNPRGXN0DsdOHyPrXBa1Qmo5ZJ2e+DmaQTKWT7du3ZK11q3tztRamzIB/YD/s93vCswp6TUJCQm6JImJiSUuM2mS1qD1vfeWuKgpSpPRGbhCTjMy7juxT4e/Hq5T0lMcsj5P/RwdTTKWD7BSF1FTzeyi6Qj0V0qlADOBq5RSX5i4vTxVqhi36ekVsTXhamoE1+Dw04f5aOVHMtSwcGumFXit9WitdS2tdW3gNmCB1vous7aXX26BP3q0IrYmXJGX8uKBlg+wPm29DDUs3JZbHgcvBV6URr2q9Vh8/2Ie+ukhackLt1QhBV5rnaQr6Bh4gPBw41YKvCiNN3u8ibeXN7uO7bI6ihAO5fYteBkTXpSkYURDJvSZQLdp3XjyNxlqWLgPtyzwAQHg7w9nz0JWltVphCtQSvHHPX9QN7yuHCcv3IZbFniQfnhRdnXC6/BQq4foOLkjLy982eo4QlwyKfBC5OPn7cf2odtpH9OebzZ+Y3UcIS6JFHghCokLi6NV9Vbc9PVNfLzyY6vjCFFuJRZ4pdRQpVR4RYRxJCnw4lJUCajCrhG7SKiRwMS/JlodR4hyKc1wwVHA30qpVcBk4Ffb6bFOTQq8uFR5Qw3/3IaYkBiua3id1ZGEKJMSW/Ba6zFAPWAScB+wTSk1TilV1+Rsl0QKvHCE3KGGw/zDeD7xeavjCFEmpeqDt7XYD9imbCAcmK2UetPEbJdECrxwlOigaBpGNOTlRS+zcv9Kq+MIUWql6YMfrpRKBt4ElgLNtNaPAgnAjSbnKzcp8MKRooKiyBydyfpD6xnxywir4whRKqVpwVcBbtBa99Jaf621Pgegtc7BGBLYKeUW+CNHrM0h3EegXyA9LuvB9HXT2XN8j9VxhChRafrgX9Ba2x2kQ2tdoZfiK4uICONWCrxwpJohNTn41EEm/jWRR+Y8YnUcIYrltsfBV6tm3B6SkWCFg3kpLx5q9RBbj2yVoYaFU5MCL0Q51KtajwX3LuD+H+9n9/HdVscRwi63LfBVqoCXl7GT9dw5q9MId/V2z7dRSpGSnmJ1FCEu4rYF3tv7Qj/84cPWZhHuq0FEA2JCYug8tTNP/faU1XGEKMBtCzxIN42oOAvvW0j9qvVZsXeF1VGEyCMFXggHqBNeh3tb3CtDDQunIgVeCAep5FOJncN30jG2I19v+NrqOEJIgRfCkWJDY4mPjueW2bfwv+T/WR1HeDgp8EI4WO5Qwy2rt2TCiglWxxEeTAq8ECaIDY2lVkgthv0yjDlb51gdR3goKfBCmCQ6KJoDTx4g0DeQMQvGWB1HeCAp8EKYKCooisaRjXl18av8k/qP1XGEh/GIAn/woLU5hGeLCooi69ksVqWuYvjPw62OIzyIWxf4qCjj9sABcP6LDAp3FuAbQO/LezNrwyz2Ht9rdRzhIdy6wAcFQUgInDkD6elWpxGermZITVKfTOXdFe/KUMOiQrh1gQeoUcO43bfP2hxCACilGJgwkB1Hd3AwU/oOhbncvsDXrGncSoEXzqJ+1frMv2c+93x/D4/NfczqOMKNeUyB37/f2hxCFPZ+7/cJ8A3g3/R/rY4i3JTbF3jpohHOqkFEA/7b4790mtJJhhoWpnD7Ai8teOHMlFIseWAJjSIa8eeeP62OI9yMaQVeKeWvlPpLKbVGKbVBKTXWrG0VR1rwwtnVDqvNnc3v5MopV/LqoletjiPciJkt+DPAVVrrFkA80FspdYWJ27NLWvDCFfj7+PPv8H/pGNuRrzZ8ZXUc4SZ8zFqx1loDmbaHvrapwk83kha8cBWxobEE+gYSMT6CjDMZPNjqQasjCRentImneCqlvIFk4HLgA631M3aWGQgMBIiKikqYOXNmsevMzMwkKCio1BmysxU9e3YG4LffFuHjY/53TFkzWsUVcnpixrPnz5Kdk03m2UyqBVZzyDo98XM0gzNm7NatW7LWurXdmVpr0ycgDEgEmha3XEJCgi5JYmJiicsUFh2tNWi9a1eZX1ou5cloBVfI6akZD2Qc0LyInrNljkPW56mfo6M5Y0ZgpS6iplbIUTRa62O2At+7IrZXWFyccbt7txVbF6LsooKiOPjUQQJ8A3juj+esjiNclJlH0UQqpcJs9wOAHsBms7ZXnNq1jduUFCu2LkT5VAusRpPIJoxbMo7VB1ZbHUe4IDNb8NWBRKXUWuBvYL7W2pJL20iBF64qd6jhv/b9JUMNizIzrcBrrddqrVtqrZtrrZtqrV8ya1slye2ikQIvXFGAbwDX1LuG2Ztms++EHA4mSs/tz2SFCy34XbssjSFEudUKqcXex/cyftl4Bv00yOo4wkV4VIGXFrxwZUopHmvzGLtP7JahhkWpeESBz+2i2bULcnKszSLEpahftT4/3/kzd317F4PnDrY6jnByHlHgK1c2rs967hykplqdRohL90HfD6jsV5kdR3dYHUU4MY8o8FCwFS+Eq6tftT5vXv0mnaZ0YuT8kVbHEU7KYwp8bj/8v3JtBeEmlFIse3AZTSKbsHT3UqvjCCfkMQX+ssuM2507rc0hhCPVDqvNrU1u5copV/La4tesjiOcjMcU+Pr1jdstW6zNIYSjBfgGsGvELjrGduTLdV9aHUc4EdOGC3Y2uQV+61ZrcwhhhtjQWCr7VqbL1C6cyj7FAy0fsDqScAIe14LfuhVMHCFZCMtEVI5g94jdNI9qzjt/vmN1HOEEPKbAR0ZCWBgcPw5paVanEcIcMaExxITE8MRvT/Dztp+tjiMs5jEFXinpphGeISooikNPHcLH20eGGvZwHlPgQQq88ByRgZE0q9aMcUvGse7gOqvjCItIgRfCTUUHRXPquVMs2bOEPSf2WB1HWEAKvBBuzN/Hn371+nHs9DH2n9hvdRxRwTyywG+25LpSQlgjJjSGZtWa8drS12SoYQ/jUQW+QQPw8jJa8GfOWJ1GiIo1pM0Q9mXsk6GGPYhHFfjKleHyy+H8eWnFC8/TIKIBc+6Yw62zb2XIvCFWxxEVwKMKPECzZsbtOjmwQHioj/t9TLBfMNuObLM6ijCZxxb4tWutzSGEVRpENGBc93FcOeVKnp7/tNVxhIk8tsBLC154MqUUfz30F82jmrMoZZHVcYRJpMAL4aHiwuK4sdGNdJnWhdeXvG51HGECjyvwl10GAQGwbx+kp1udRghr5Q01HNOR6WunWx1HOJjHFXhvb2ja1Li/Zo21WYRwBrGhsTSKbMRd393FlH+mWB1HOJDHFXiAhATj9u+/rc0hhLPIHWq4abWmvLXsLavjCAfxyALfpo1xKwVeiAtiQmOICY3hqflP8ev2X62OIxxACrwQIk90UDRpI9NAwajfR1kdR1wijyzwjRoZZ7WmpMjFP4QoLKJyBPFR8YxfNp71h9ZbHUdcAo8s8D4+0KqVcX/lSmuzCOGMooKiyHo2i6SUJIbOG2p1HFFOHlngAVq3Nm6lm0YI+yr5VOK6BtcxZ9scGWrYRflYHcAquf3wf/1lbQ4hnFlMaAw7h+1kyLwhnNfn+ajfR1ZHEmXgsS34Dh2M26VLISfH2ixCODOlFEPbDSU1M5UDGQesjiPKwLQCr5SKUUolKqU2KqU2KKWGm7Wt8qhdG2Jj4dgxWC/7kYQoVsOIhvxw2w/cPPtm6ZN3IWa24LOBJ7XWjYErgMFKqcYmbq/MOnc2bhcutDaHEK5icv/JhPqHsvWwXPfSFZhW4LXWqVrrVbb7GcAmoKZZ2yuPLl2M20UymJ4QpVKvaj1e6vYSHad05Jn5z1gdR5RAaa3N34hStYFFQFOt9YlC8wYCAwGioqISZs6cWey6MjMzCQoKckiuPXsCuOeedoSHn+Wbb5ahlENW69CMZnKFnJLRMRyd8ez5s2SezcTP248gP8es1xM/R0fo1q1bsta6td2ZWmtTJyAISAZuKGnZhIQEXZLExMQSlymtnByto6K0Bq03bXLYah2a0UyukFMyOoYZGTPPZGpeRL+x5A2HrM9TP8dLBazURdRUU4+iUUr5At8A07XW35q5rfJQ6kI3zYIF1mYRwtUE+gWSMjyFjjEd+XzN51bHEXaYeRSNAiYBm7TWb5u1nUvVs6dx+6uMrSREmcWFxVG/an3u+f4ePlvzmdVxRCFmtuA7AncDVymlVtuma0zcXrn06mXc/vEHnD1rbRYhXFFkYCR7Ht9Do4hGjF863uo4Ih8zj6JZorVWWuvmWut42zTPrO2VV61axgVATp40TnoSQpRdrZBaxIbG8vTvTzN/x3yr4wgbjz2TNb8+fYzbn3+2NocQriwqKIrDIw9zXp+XQyidhBR4oHdv41YKvBCXpmrlqsRHx/PWn2+xMW2j1XE8nhR44MorISTEGLJg+3ar0wjh2qKDosl6Lov5O+bLsAYWkwIP+PnBtdca97/5xtosQrgDP28/BjQcwM/bfyY1I9XqOB5LCrzNjTcat7NnW5tDCHcRFxbHtqHbGLtwLIN+GmR1HI8kBd6md28IDDSu8LRrl9VphHAPSilGXDGCI6eOyFDDFpACbxMQANfYjtKXbhohHKdhRENm3zKbG766gWE/D7M6jkeRAp/PLbcYt5/LWddCONy0AdMI9w9ny+EtVkfxGFLg87n2WggPh9WrjUkI4Tj1qtbjha4v0H5Se0b/PtrqOB5BCnw+lSrBHXcY96dNszaLEO7IS3nxz6B/iK8ezx87/7A6jtuTAl/IffcZt9Onw7lzlkYRwi3FhcXRr14/rv78ahm7xmRS4AtJSIAmTSAtDX76yeo0QrinQL9Ado3YRcfYjkxbLT+XzSIFvhClYOBA4/6ECdZmEcKdxYbGUq9KPe774T4ZT94kUuDtuO8+CAqCpCRYu9bqNEK4r9yhhhtGNORAphwn72hS4O0ICYH77zfuSyteCHPlDjW8L2Of7Hh1MCnwRRhqGyPpiy/g8GFrswjh7qKCooiPiud09mmenv+01XHchhT4ItSrB/36wenT8LbTXnBQCPfh7eVNQo0E3l3+LpvTNlsdxy1IgS/GmDHG7YQJcOSItVmE8ATRQdFkPpvJvO3zGDJviNVxXJ4U+GK0a2dcszUzE955x+o0QngGP28/bmx0I/N3zpcByi6RFPgSPP+8cfv++3D0qLVZhPAUcWFxbB68mf8k/keGGr4EUuBL0KED9OgBGRnw8stWpxHCcyileLLDkxw7fUwuGlJOUuBL4c03jROgJk6ErVutTiOE52gY0ZBZN8+i/8z+DP95uNVxXI4U+FKIjzeOi8/OhpEjrU4jhOeZccMMqlauyqa0TVZHcSlS4EvplVeMKz79+CPMnWt1GiE8S72q9Xiu03N0mNyBZ/941uo4LkMKfClVrw5jxxr3H33UOLJGCFFxvL28WfPIGlpVb8XvO363Oo5LkAJfBsOHG6NN7tlz4Rh5IUTFiQ2NpfflvenxRQ/eWvaW1XGcnhT4MvDxgf/9D7y9jcMmk5KsTiSE5wnyC2LXiF10iOnA1NVTrY7j1KTAl1HLlvDss6A13H23HBsvhBViQ2OpW6Uu9/9wPzPWzbA6jtOSAl8Ozz8P7dvD3r3w8MNGsRdCVKxqgdXY8/ge6obX5bXFr1kdxylJgS8HHx/jkn7BwfDttzKMgRBWqRVSi9phtXl2wbMk/ZtkdRynIwW+nOrUgSlTjPsjR8L8+dbmEcJTRQVFcfTpo2SczWDkfDlRJT8p8JfgxhuNo2lycuDWW+UsVyGsEh4QTpuabZiwYgJbDm+xOo7TMK3AK6UmK6UOKaXWm7UNZzB2LFx7LaSnGyNP7t9vdSIhPFN0UDQZozP4ccuPMtSwjZkt+KlAbxPX7xS8vGDGDGjbFlJSoHdvyMz0sTqWEB7J19uXm5vczB///iFDDWNigddaLwI84iDCoCBj+IIGDWDdOnjmmWYcP251KiE8U+2w2mx8bCOj/hjl8UMNK23iMX5KqdrAHK1102KWGQgMBIiKikqYOXNmsevMzMwkKCjIkTEd5uDBSgwf3pKDB/1p0OAEb765lpCQbKtjFcmZP8tcktExPDHj6ezTpGamUiukFr5evg5ZpzN+jt26dUvWWre2O1NrbdoE1AbWl3b5hIQEXZLExMQSl7FSSorWNWpkadC6RQutU1OtTlQ0Z/8stZaMjuLJGRM+TtDD5g1zyLqc8XMEVuoiaqocReNgcXHw7rurqV8f1qwxLvu3YYPVqYTwXDNvmkm1oGpsOOR5/xGlwJsgMvIMixfDFVfA7t3GVaHkOHkhrHF5lcsZ1XEUHSZ34Lk/nrM6ToUy8zDJL4E/gQZKqb1KqQfN2pYzqlYNFiyAm26CEyeMo2vGjTOOmRdCVCxvL2/WPbqO1jVa89v236yOU2HMPIrmdq11da21r9a6ltZ6klnbclYBATBr1oWToZ57zjhm/sgRq5MJ4XliQ2Ppfll3ek3vxTt/esb4ItJFYzIvL+Ni3XPnQpUqMG8eNGtm3AohKlZIpRBShqfQIaYDk1a5f5tTCnwFueYa+Ocf6NgRUlOhb1946CGj+0YIUXHiwuKoE16Hh356iC/XfWl1HFNJga9AsbGwcCGMHw+VKsGkSdCoEcycKUMOC1GRqgVWY+/je7ks/DLGLR5ndRzTSIGvYN7e8NRTsGqVcQjl/v1w++3QvbscTilERaoZUpPaYbV5bsFzLExZaHUcU0iBt0jjxrBsGXz6KVStComJ0Lw5PPCAcWilEMJ8UUFRpD+TTvrpdLccalgKvIW8vODBB41hhgcPNh5PmQL168MTT8ABGStJCNOF+YfRrmY7Jv41kW1Htlkdx6GkwDuBKlVg4kTYtAluuw3OnDGuElW7NgwaBNu3W51QCPdWPbg6GaMzmL1pNoPnDrY6jsNIgXcil18OX35p9M9ff71R6D/5xBil8pZb4M8/ZWesEGbx8fLhtia3sXj3Yg5mHrQ6jkNIgXdCLVsa13rduBHuv9/YMfv118aQBy1awP/9nxxeKYQZ6oTXYe2jaxk5f6RbDDUsBd6JNWoEkyfDzp3wzDMQGWmMNz94MNSoYRxHn5Qkwx8I4WjPdnqWrOws9p9w7Uu0SYF3AbVqweuvw549RhdO165w8qRxHH23bsbx9SNHwurV0oUjhCM0jGjI59d/Tt8v+zLilxFWxyk3KfAupFIlYydsYqKxQ/bZZ40dsfv2wX//a3TtNGwITz8NS5fC+fNWJxbCtc2+eTbRQdGsO7jO6ijlIgXeRTVsCK++anTfLF1qdNtERBiHXI4fD1deCdHRRh/+t9/CsWNWJxbC9dStUpenOjxF+0ntGbNgjNVxykwKvItTytj5OnGiMcZNUhI8/jhcdhkcPgxTp8KNNxonU11xhTGy5cKFxhE6QoiS+Xj5sHHwRtrWbMuJM651dIMUeDfi4wNdusDbbxvHzm/YYIxB36mTcRLVihVGq79rV+PY+6eeas6LLxoXI8nIsDq9EM4rNjSWrrW7su3oNt5b/p7VcUrNx+oAwhxKGcMhNG4Mo0dDZiYsWgS//24U9PXrITm5CsnJxvJeXsYhmB07Gi39hATjjFovaQIIARhDDTer1oywmDAmrZrEg62c/xpGUuA9RFCQMWTxNdcYjw8cgI8/Xs/x401ZssQYyjh3mjjxwmtatjSKfe5Uv75xXL4QnsjP24/aYbVp92k7gvyCuLXprVZHKpYUeA8VHQ1duhyma1fj8cmT8PffsGQJrFwJycmwdy8sXmxMuSpXNn4VNGkCTZsat02aQEyM8atBCHeXO9Tw7uO7eXXRqzzX2Xmv8yoFXgAQGGj0zecWfIBDh4xhE5KTL0y7dxtfACtXFnx9SMiFwl+v3oWpbl3jS0EId1IzpCbeXt6MmTyGLnFduDLuSqsj2SUFXhSpWjXjYuG9e194Lj3d2Hm7fv2F2/XrjSN2li83psJq1TKK/eWXXyj6cXHGVLWqtPyFa4oOiib9mXT+2PkHT/72JG/1fMvqSBeRAi/KJDzcOMb+ykINlkOHjIK/aRNs23Zh2rnT6OrZu9c4QauwwMALxd7eJCdrCWcW5h9Gh5gO3Pv9vTzW+jHqVqlrdaQCpMALh6hWzZi6dSv4fHY27NpVsOj/+6/xXEqKcXjmxo3GZI+XVxeio42xd/JPNWsWfCy/BIRVqgdX59ioY7y+5HVSM1L5oO8HVkfKIwVemMrHx+iSqVu3YFcPGOPmHDtmFPuiprQ0xf79xqUNi+PnZ+w4rlbNGJQt9wunqMf+/qa9ZeGBfLx8uLPZndzw1Q0czDxIVFCU1ZEAKfDCQkoZXT7h4RAfb3+Z+fMX0qBBl7wib2/at8/4oti9u/SXOwwONop9RIRx0ldpprAw4wtLCHvqhNfhn0H/cMc3dxBSKYSP+n1kdSQp8MK5+fpqYmONETOLk5VlHNuflmbsD8i9LXw/93FGhjHt2FG2PKGhBYt+aChkZTXgxx+N+6GhxhFF9u6Hhhq/HKQryb39p/N/eGPpG+w7sY+aITUtzSIFXriFypWN8Xcuu6zkZbWG48eNYn/kCBw9WropPd143fHjxn6EC6ozb17pcvr4XFz8g4ONk8oKT4GB9p/PP1WuLGcbO5tGkY2YOmAqTf+vKT0u68E7vd+xLIsUeOFxlDK6W8LCyva6nByjuOcW/CNHjCtr/fXXFqKjG3DixIUvgOPHKfA49/6ZM8brjhxx3PupXNl+4a9cGQICjCk9vR5z5lx4rqy3fn7yy6OsfrjtB77b/B1rDqyhRXSLAvNOnTvFuZxzhFQKMTWDFHghSsnL68I+g7r5joarVi2Vrl0blGodZ85w0RdBZqZxJnFmZumn3OVPnjS6p7KyjF8kRbu0rgKl7Bd/f3/jOgWVKl24X/i2tPM2bgwhJKToZXx8XOtLpm6Vuoy4YgShr4fyxBVP8PJVL+fN+2LdF3yx9gsW3rfQ1AxS4IWoQJUqGUfxREY6Zn05OUZxz1/8MzLg1Cnj+dzbtWu3UbNmvYueP3Xq4mXt3Z47Z3yZnDzpmNz2tSp2rlJGoffzuzD5+hZ8bPZzGzaEUrnyhed8fYufvL182DR4E2sPrmXu1rl0rd2ViX9N5K0/36JDTAczP0xACrwQLs3L60K3THGSkvbRtWu9cm8nO9v+l8Lp08avkjNnLtwvfFvaeYcOnaBSpZAiX3f+/IVtW6dlmV/h6xuLr28MWeeP418ph5x+qzhbP425W+eafgasFHghRIl8fIydwcHB5m0jKWkVXfMPhlRIdrZR7M+dg7NnC06FnyvpcXlfc/jwMQICwi5a7tw5I1/u/dwpJyf3vgLCOH0GOGecnp2ts2lYtaF5HyhS4IUQLsLHx/rzEJKSVhf7JVRYboG/9osbWLF7FSeysqDShatCfbHuC7rV6cblVS43Ia3JV3RSSvVWSm1RSm1XSo0yc1tCCOFsvLzgz9QkVqT9wQmvXRCUBr4Xrpe5bPcyNqRtMG/7Zq1YKeUNfAD0ARoDtyulGpu1PSGEcEYZZzLoWbcnAxoOwEcV/AmSrbPJPJNp2rbN/MHTFtiutd4JoJSaCVwHFDGslBBCuJ9rG1zLtQ2uBeDp+U9Tr0o9ZqyfwZJdS8jW2Yz6fRR1q9TlilpXOHzbZhb4msCefI/3Au1M3J4QQji1N3u8CUD3y7qz9uBass5lMfyX4fh5+ZmyPaW1NmfFSt0E9NZaP2R7fDfQTms9pNByA4GBAFFRUQkzZ84sdr2ZmZkElXRMmMVcISO4Rk7J6BiS0THMyJh1LosA3wAU5TuLq1u3bsla69Z2Z2qtTZmA9sCv+R6PBkYX95qEhARdksTExBKXsZorZNTaNXJKRseQjI7hjBmBlbqImmrmUTR/A/WUUnWUUn7AbcCPJm5PCCFEPqb1wWuts5VSQ4BfAW9gstbavOOBhBBCFGDqaQNa63lAKQdSFUII4UgykrQQQrgpKfBCCOGmpMALIYSbkgIvhBBuSgq8EEK4KSnwQgjhpkwbqqA8lFJpwK4SFosADldAnEvhChnBNXJKRseQjI7hjBnjtNZ2LwLpVAW+NJRSK3VR4y44CVfICK6RUzI6hmR0DFfImJ900QghhJuSAi+EEG7KFQv8J1YHKAVXyAiukVMyOoZkdAxXyJjH5frghRBClI4rtuCFEEKUgksVeKVUb6XUFqXUdqXUKKvzFKaUmqyUOqSUWm91lqIopWKUUolKqY1KqQ1KqeFWZypMKeWvlPpLKbXGlnGs1ZmKopTyVkr9o5SaY3WWoiilUpRS65RSq5VSK63OY49SKkwpNVsptVkptUkp1d7qTPkppRrYPr/c6YRSaoTVuUriMl00SilvYCvQA+P6rn8Dt2utneYi3kqpzkAm8JnWuqnVeexRSlUHqmutVymlgoFkYICTfY4KCNRaZyqlfIElwHCt9XKLo11EKfUE0BoI0Vr3szqPPUqpFKC11trZjt/Oo5SaBizWWn9qu0BQZa31MYtj2WWrRfswLkFa0nk7lnKlFnxbYLvWeqfW+iwwE7jO4kwFaK0XAUetzlEcrXWq1nqV7X4GsAnjAulOw3YlskzbQ1/b5HQtEaVULaAv8KnVWVyZUioU6AxMAtBan3XW4m7THdjh7MUdXKvA1wT25Hu8FycrTK5GKVUbaAmssDjKRWxdH6uBQ8B8rbXTZQTeBZ4GcizOURIN/KaUSrZd5N7Z1AHSgCm27q5PlVKBVocqxm3Al1aHKA1XKvDCgZRSQcA3wAit9Qmr8xSmtT6vtY4HagFtlVJO1eWllOoHHNJaJ1udpRSu1Fq3AvoAg21dic7EB2gFfKi1bgmcBJxuHxuArfuoP/C11VlKw5UK/D4gJt/jWrbnRBnZ+rW/AaZrrb+1Ok9xbD/VE4HeFkcprCPQ39a/PRO4Sin1hbWR7NNa77PdHgK+w+judCZ7gb35fqXNxij4zqgPsEprfdDqIKXhSgX+b6CeUqqO7Vv0NuBHizO5HNsOzEnAJq3121bnsUcpFamUCrPdD8DYsb7Z0lCFaK1Ha61raa1rY/wtLtBa32VxrIsopQJtO9OxdXv0BJzqKC+t9QFgj1Kqge2p7oDT7PQv5HZcpHsGTL7otiNprbOVUkOAXwFvYLLWeoPFsQpQSn0JdAUilFJ7gRe01pOsTXWRjsDdwDpbHzfAs7YLpDuL6sA029EKXsBXWmunPQzRyUUB3xnf6/gAM7TWv1gbya6hwHRb420ncL/FeS5i+4LsAQyyOktpucxhkkIIIcrGlbpohBBClIEUeCGEcFNS4IUQwk1JgRdCCDclBV4IIdyUFHghhHBTUuCFEMJNSYEXoghKqTZKqbW28ekDbWPTO9WYOEIUR050EqIYSqlXAH8gAGO8lNcsjiREqUmBF6IYtlPn/wZOAx201uctjiREqUkXjRDFqwoEAcEYLXkhXIa04IUohlLqR4zhgOtgXOpwiMWRhCg1lxlNUoiKppS6BzintZ5hG9lymVLqKq31AquzCVEa0oIXQgg3JX3wQgjhpqTACyGEm5ICL4QQbkoKvBBCuCkp8EII4aakwAshhJuSAi+EEG5KCrwQQrip/wd0h55zJvi8WwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#################################\n",
    "####### Solution 1.3 ############\n",
    "#################################\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(-2, 2, 400)\n",
    "\n",
    "# Parametric equations\n",
    "x = np.exp(t)\n",
    "y = np.exp(-t)\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(x, y, label='Curve: α(t) = (e^t, e^{-t})', color='blue', linewidth=2)\n",
    "\n",
    "# Add arrows to indicate the direction of traversal\n",
    "arrow_start = (x[0], y[0])  # Starting point\n",
    "arrow_end = (x[399], y[399])    # Ending point\n",
    "arrow_dx = arrow_end[0] - arrow_start[0]\n",
    "arrow_dy = arrow_end[1] - arrow_start[1]\n",
    "\n",
    "plt.arrow(arrow_start[0], arrow_start[1], arrow_dx, arrow_dy, head_width=0.2, head_length=0.2, fc='green', ec='green', \n",
    "          linestyle=\"dotted\", label='Direction of Traversal')\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Parametric Curve α(t) = (e^t, e^{-t})')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.axis('equal') \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "da5a2e95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###########################\n",
    "######  Solution 1.4  #####\n",
    "###########################\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(-5 * np.pi, 5 * np.pi, 1000)  \n",
    "\n",
    "# Parametric equations\n",
    "x = np.cos(t)\n",
    "y = np.sin(t)\n",
    "z = t\n",
    "\n",
    "# Create the 3D plot\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z, label='Curve: α(t) = (cos t, sin t, t)', color='blue', linewidth=2)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.set_title('Solution 1.4: Parametric Curve α(t) = (cos t, sin t, t)')\n",
    "\n",
    "ax.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a87809ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "######################################\n",
    "##########  Solution 1.5  ############\n",
    "######################################\n",
    "\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(-5 * np.pi, 5 * np.pi, 1000)  \n",
    "\n",
    "# Parametric equations\n",
    "x = np.cos(t)\n",
    "y = np.sin(t)\n",
    "z = -t\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z, label='Curve: α(t) = (cos t, sin t, -t)', color='blue', linewidth=2)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.set_title('Parametric Curve α(t) = (cos t, sin t, -t)')\n",
    "ax.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "df2a2f97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##############################\n",
    "####### Solution 1.6  ########\n",
    "##############################\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(-5 * np.pi, 5 * np.pi, 1000) \n",
    "\n",
    "# Parametric equations\n",
    "x = np.sin(t)\n",
    "y = np.cos(t)\n",
    "z = t\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z, label='Curve: α(t) = (sin t, cos t, t)', color='blue', linewidth=2)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.set_title('Parametric Curve α(t) = (sin t, cos t, t)')\n",
    "ax.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0ad2d9f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# parameter range\n",
    "t = np.linspace(-5 * np.pi, 5 * np.pi, 1000)  \n",
    "\n",
    "# Parametric equations\n",
    "x = np.sin(t)\n",
    "y = np.cos(t)\n",
    "z = -t\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z, label='Curve: α(t) = (sin t, cos t, -t)', color='blue', linewidth=2)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.set_title('Parametric Curve α(t) = (sin t, cos t, -t)')\n",
    "ax.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7dd26ae9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#####################################\n",
    "#########  Solution 1.8   ###########\n",
    "#####################################\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# parameter range\n",
    "t = np.linspace(-5 * np.pi, 5 * np.pi, 1000) \n",
    "\n",
    "# Parametric equations\n",
    "x = np.cos(t)\n",
    "y = np.sin(t)\n",
    "z = 2 * np.cos(t)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z, label='Curve: α(t) = (cos t, sin t, 2cos t)', color='blue', linewidth=2)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "ax.set_title('Parametric Curve α(t) = (cos t, sin t, 2cos t)')\n",
    "ax.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1181081",
   "metadata": {},
   "source": [
    "-----------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af135c72",
   "metadata": {},
   "source": [
    "<b>In Exercises 1.9 - 1.12, find a paramatetrized of the given curve:</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4ea626d",
   "metadata": {},
   "source": [
    "<b>1.9</b> The portion of the parabola $y = x^2$ in $\\mathbb{R}^2$ with  $-1 \\le x \\le 1$\n",
    "\n",
    "<b>1.10</b> The portion of the curve $xy = 1$ in $\\mathbb{R}^2$ with $1 \\le x \\le 2$\n",
    "\n",
    "<b>1.11</b> The circle $x^2 + y^2 = a^2$ in $\\mathbb{R}^2$ traversed once in the clockwise direction\n",
    "\n",
    "<b>1.12</b> A right-handed helix in $\\mathbb{R}^3$ that:<br>\n",
    "(a) lies on the circular cylinder of radius 2 whose axis is the z-axis<br>\n",
    "(b) completes one complete twist as it rises from $z = 0$ to $z = 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0176ef9f",
   "metadata": {},
   "source": [
    "<b> Solution 1.9</b>\n",
    "\n",
    "Here, range is between $-1$ and 1<br>\n",
    "and, if $x = t, y = t^2$\n",
    "\n",
    "Thus, parametrization: $\\alpha: [-1,1] \\to \\mathbb{R}^2, \\alpha(t) = (t, t^2)$\n",
    "\n",
    "<b>Solution 1.10</b>\n",
    "\n",
    "Here, range is between 1 and 2<br>\n",
    "and, if $x = t, y = \\frac{1}{t}$\n",
    "\n",
    "Thus, parametrization:  $\\alpha: [1,2] \\to \\mathbb{R}^2, \\alpha(t) = (t, \\frac{1}{t})$\n",
    "\n",
    "<b>Solution 1.11</b>\n",
    "\n",
    "Given circle equation $x^2 + y^2 = a^2$ can be written as $(\\frac{x}{a})^2 + (\\frac{y}{a})^2 = 1$\n",
    "\n",
    "To parametrize circle, we use:<br>\n",
    "$cos^2 \\, t + sin^2 \\, t = 1$ where $t$ is the angle\n",
    "\n",
    "$\\Rightarrow \\frac{x}{a} = cost \\, t, \\quad \\frac{y}{a} = sin \\, t$\n",
    "\n",
    "$\\Rightarrow x = a\\, cos \\, t \\quad y = a \\, sin \\, t\\quad$ where $a \\gt 0$\n",
    "\n",
    "But, we need it in clockwise direction, therfore $t$ should be negative<br>\n",
    "$\\Rightarrow x = a\\,cos\\,(-t)$ and $y = a\\,sin\\,(-t)$\n",
    "\n",
    "Thus, parametrization: $\\alpha : \\mathbb{R} \\to \\mathbb{R}^2, \\alpha(t) = (a\\,cos (-t), a\\,sin(-t))$\n",
    "\n",
    "or <b>parametrization: $\\alpha : \\mathbb{R} \\to \\mathbb{R}^2, \\alpha(t) = (a\\,cos\\,t, a\\,- sin\\,t)$</b>\n",
    "\n",
    "\n",
    "<b>Solution 1.12</b>\n",
    "\n",
    "Since, radius$ = 2$ and helix axis is $z-$axis, $x$ and $y-$coordinate will satisfy circular equation such that<br>\n",
    "$x = 2 cos\\,t$,<br>\n",
    "$y = 2 sin\\, t$ and $z = bt$\n",
    "\n",
    "Since, $z$ complete one twist, it means it increase from 0 to $2\\pi \\Rightarrow b = 2\\pi$.\n",
    "\n",
    "Thus, parametrization : $\\alpha : \\mathbb{R} \\to \\mathbb{R}^3,\\quad \\alpha(t) = (2 cos\\,t, 2 sin\\,t, 2\\pi t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87dcd03d",
   "metadata": {},
   "source": [
    "----------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66869c9e",
   "metadata": {},
   "source": [
    "<b> 1.13</b> Find a parametrization of the line in $\\mathbb{R}^3$ that passes through the point $a = (1, 2, 3)$ and is parallel to $v = (4, 5, 6)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c51c3e0b",
   "metadata": {},
   "source": [
    "<b>Solution</b>\n",
    "\n",
    "Since point $a = (1,2,3)$ is parallel to $v = (4,5,6)$<br>\n",
    "Parametrization is simple:<br>\n",
    "$\\alpha(t) = (1,2,3) + t(4,5,6)$<br>\n",
    "$\\Rightarrow \\alpha(t) = (1 + 4t, 2 + 5t, 3 + 6t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e3776f2",
   "metadata": {},
   "source": [
    "<b>1.14</b> Let $l$ be the line in $\\mathbb{R}^3$ parametrized by $\\alpha(t) = (1 + 2t, -3t, 4 + 5t)$. Find a point that lies on $l$ and a vector that is parallel to $l$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfc6e985",
   "metadata": {},
   "source": [
    "<b>Solution</b> \n",
    "\n",
    "Finding a point that lies on $l$ is simple:\n",
    " Let $t = 1$, then<br>\n",
    " point,$p$ would be $(1 + 2(1), -3(1), 4 + 5(1))$<br>\n",
    " $\\Rightarrow point, p : (3,-3,9)$\n",
    " \n",
    " To find vector parallel to line, we can simply take coefficients of $t$ in parametric equation, or derivatives to be precise.\n",
    " \n",
    " Thus, $vector, v : (2, -3, 5)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8121b716",
   "metadata": {},
   "source": [
    "<b>1.15</b> Find a parametrization of the line in $\\mathbb{R}^3$ that passes through the point $a = (1,0,0)$ and $b=(0,0,1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72a47a6d",
   "metadata": {},
   "source": [
    "<b>Solution </b>\n",
    "\n",
    "Line that passes through $a = (1,0,0)$ and $b = (0,0,1)$ would be parallel to $v$ given by $\\overrightarrow{ab} = b - a$\n",
    "\n",
    "$i.e., (0,0,1) - (1,0,0) = (-1,0,1)$\n",
    "\n",
    "Thus, parametrization: $\\alpha(t) = (1, 0 , 0) + t(-1, 0, 1)$\n",
    "\n",
    "$\\Rightarrow$ parametrization: $\\alpha(t) = (1 -t, 0, t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8a55d35",
   "metadata": {},
   "source": [
    "<b>1.16</b> Find a parametrization of the line in $\\mathbb{R}^3$ that passes through the points $a = (1, -2, 3)$ and $b = (-4, 5, -6)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a2c9c85",
   "metadata": {},
   "source": [
    "<b> Solution </b>\n",
    "\n",
    "Line that passes through the points $a = (1, -2, 3)$ and $b = (-4, 5, -6)$ would be parallel to $v$ given by: $\\overrightarrow{ab} = b - a$\n",
    "\n",
    "i.e, $(-4, 5, -6) - (1, -2, 3) = (-5, 7, -9)$\n",
    "\n",
    "Thus, parametrization: $\\alpha(t) = (1, -2, 3) + t(-5, 7, -9)$\n",
    "\n",
    "$\\Rightarrow$ parametrization :$ \\alpha(t) = (1 - 5t, -2 + 7t ,3 -9t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2e3f5db",
   "metadata": {},
   "source": [
    "<b>1.17</b> Let $l$ be the line in $\\mathbb{R}^n$ parametrized by $\\alpha(t) = a + tv$, and let $p$ be a point in $\\mathbb{R}^n$. Suppose that $q$ is the foot of the perpendicular dropped from $p$ to $l$.<br>\n",
    "<b>(a)</b>Since $q$ lies on $l$, there is a value of $t$ such that $q = a + tv$. Find a formula for $t$ in terms of $a, v$, and $p$. (Hint: $l$ lies in a direction perpendicular to $p-q$)<br>\n",
    "<b>(b)</b> Find a formula for the point $q$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc8415fc",
   "metadata": {},
   "source": [
    "<b> Solution (a)</b>\n",
    "\n",
    "Since $l$ lies in the direction perpendicular to $(p-q)$<br>\n",
    "$\\Rightarrow$ vector, $v$ which lies on $l$ is perpendicular to (or orthogonal to) $(p-q)$\n",
    "\n",
    "Therefore, using dot product, we have:<br>\n",
    "$v \\cdot (p-q) = 0$\n",
    "\n",
    "We know that, $q = a + tv$<br>\n",
    "Then, <br>\n",
    "$v \\cdot (p - (a + tv)) = 0$\n",
    "\n",
    "$\\Rightarrow v \\cdot (p - a - tv) = 0$<br>\n",
    "$\\Rightarrow (v \\cdot p) - (v \\cdot a) - (v\\cdot tv) = 0$<br>\n",
    "$\\Rightarrow (v\\cdot tv) = (v \\cdot p) - (v \\cdot a)$<br>\n",
    "\n",
    "$\\Rightarrow t(v \\cdot v) = v(p - a)$\n",
    "\n",
    "$\\Rightarrow t = \\frac{v (p - a)}{v \\cdot v}$\n",
    "\n",
    "\n",
    "<b>Solution(b)</b>\n",
    "\n",
    "We know that, $q = a + tv$ and we have now, $t = \\frac{v (p - a)}{v \\cdot v}$\n",
    "\n",
    "Therefore, we get, <br>\n",
    "the point, <b>$q = a + t = \\frac{v (p - a)}{v \\cdot v} v$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "724b547f",
   "metadata": {},
   "source": [
    "<b>1.18</b> let $l$ and $m$ be lines in $\\mathbb{R}^3$ parametrized by:\n",
    "\n",
    "$\\alpha(t) = a + tv$ and $\\beta(t) = b + tw$\n",
    "\n",
    "respectively, where $a = (a_1, a_2, a_3), v = (v_1, v_2, v_3), b =(b_1, b_2, b_3)$ and $w = (w_1, w_2, w_3)$\n",
    "\n",
    "<b>(a)</b> Explain why the problem of determining whether $l$ and $m$ intersect in $\\mathbb{R}^3$ amounts to solving a system of three equations in two unknowns $t_1$ and $t_2$\n",
    "\n",
    "<b>(b)</b> Determine whether the lines parametrized by $\\alpha(t) = (-1, 0, 1) + t(1, -3, 2)$ and $\\beta(t) = (1, 5, 4) + t(-1, 1, 6)$ intersect by writing down the corresponding system of equations, as described in part(a), and solving the system.\n",
    "\n",
    "<b>(c)</b>Repeat for the lines parametrized by $\\alpha(t) = (2, 1, 0) + t(0,0,1)$ and $\\beta(t) = (0, 1, 3) + t(1,0,0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c369da50-1e22-419d-8345-c9d1fb5d7437",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b>\n",
    "\n",
    "Determining if two lines $l$ and $m$ intersect in $\\mathbb{R}^n$ requires two distinct parameters $t_1$ and $t_2$ for which $\\alpha + tv$ and $\\beta + tw$ can coincide.\n",
    "\n",
    "$\\Rightarrow$ given $a = (a_1, a_2, a_3), v = (v_1, v_2, v_3), b =(b_1, b_2, b_3)$ and $w = (w_1, w_2, w_3)$, we need to solve three systems of equations :\n",
    "$$a_1 + t_1 v_1 = b_1 + t_2 w_1$$\n",
    "$$a_2 + t_1 v_2 = b_2 + t_2 w_2$$\n",
    "$$a_3 + t_1 v_3 = b_3 + t_2 w_3$$\n",
    "\n",
    "$\\Rightarrow$ If any values for $t_1$ and $t_2$ satisfy all three equations, solutions exists, otherwise doesn't.\n",
    "\n",
    "\n",
    "<b>Solution (b)</b>\n",
    "\n",
    "Using values from  $\\alpha(t) = (-1, 0, 1) + t(1, -3, 2)$ and $\\beta(t) = (1, 5, 4) + t(-1, 1, 6)$ , we get three system of equations as:\n",
    "\n",
    "$$-1 + t_1(1) = 1 + t_2(-1)$$\n",
    "$$0 + t_1(-3) = 5 + t_2(1)$$\n",
    "$$1 + t_1(2) = 4 + t_2(6)$$\n",
    "\n",
    "$\\Rightarrow$ we have:<br>\n",
    "$$-1 + t_1 = 1 - t_2\\qquad\\qquad..eq(1)$$\n",
    "$$-3t_1 = 5 + t_2\\qquad\\qquad..eq(2)$$\n",
    "$$1 + 2t_1 = 4 + t_2\\qquad\\qquad..eq(3)$$\n",
    "\n",
    "From, $eq(1)$ we have $t_1 = 2- t_2$<br>\n",
    "and from $eq(2)$, we get <br>\n",
    "$$-3(2 - t_2) = 5 + t_2$$\n",
    "$$\\Rightarrow -6 + 3t_2 = 5 + t_2$$\n",
    "$$\\Rightarrow 3t_2 - t_2  = 5 + 6$$\n",
    "$$\\Rightarrow t_2 = \\frac{11}{2}$$\n",
    "\n",
    "Therefore, $t_1 = 2- t_2 = 2 - \\frac{11}{2} = -\\frac{7}{2}$\n",
    "\n",
    "But, these values of $t_1$ and $t_2$ when used on $eq(3)$, does not satisfy the equality.\n",
    "\n",
    "Hence, lines parametrized by $\\alpha(t) = (-1, 0, 1) + t(1, -3, 2)$ and $\\beta(t) = (1, 5, 4) + t(-1, 1, 6)$ do not intersect.\n",
    "\n",
    "\n",
    "<b>Solution(c)</b>\n",
    "\n",
    "Using values from $\\alpha(t) = (2, 1, 0) + t(0,0,1)$ and $\\beta(t) = (0, 1, 3) + t(1,0,0)$, we get three system of equations:\n",
    "\n",
    "$$2 + t_1(0) = 0 + t_2(1)$$\n",
    "$$1 + t_1(0) = 1 + t_2(0)$$\n",
    "$$0 + t_1(1) = 3 + t_2(0)$$\n",
    "\n",
    "$\\Rightarrow$ solving these equations we have, <br>\n",
    "$$2 = t_2$$\n",
    "$$1 = 1$$\n",
    "$$t_1 = 3$$\n",
    "\n",
    "There values of $t_1=3$ and $t_2 = 2$ will satisfy all three systems of equations for lines $l$ and $m$. <br>\n",
    "Therefore, we can say with $\\alpha(t) = (2, 1, 0) + t(0,0,1)$ and $\\beta(t) = (0, 1, 3) + t(1,0,0)$ parametrization lines $l$ and $m$ intersect."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deeccee7",
   "metadata": {},
   "source": [
    "-----------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2ab6c24",
   "metadata": {},
   "source": [
    "<h3>Section 2: Velocity, Acceleration, Speed, Arclength</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42cbbb7",
   "metadata": {},
   "source": [
    "<b>2.1</b><br>\n",
    "Let $\\alpha(t) = (t^3, 3t^2, 6t)$\n",
    "\n",
    "<b>(a)</b> Find the velocity, speed, and acceleration<br>\n",
    "<b>(b)</b> Find the arclength from $t = 0$ to $t = 4$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1fa516c-c9c2-4371-b237-5650f4de1e0c",
   "metadata": {},
   "source": [
    "We know that, <br>\n",
    "<b>Velocity : $ V(t) = \\alpha'(t)$</b> | <b>Acceleration : $\\alpha(t) = \\alpha''(t)$</b> | <b>Speed : $v(t) = \\lVert V(t) \\rVert $</b> | \n",
    "<b>arclength : $ = \\int_a^b v(t)\\,dt$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b213353d-8035-4088-88d8-f7e53efcd9ef",
   "metadata": {},
   "source": [
    "<b>Solution(a)</b><br>\n",
    "\n",
    "Here, $\\frac{d}{dt} t^3 =3t^2$, $\\quad \\frac{d}{dt}3t^2 = 3\\frac{d}{dt}t^2 = 6t\\quad$ and $\\frac{d}{dt}6t = 6$<br>\n",
    "\n",
    "Therefore, velocity, $V(t)$ or $\\alpha'(t) = (3t^2, 6t, 6)$\n",
    "\n",
    "Next, speed is $\\lVert V(t) \\rVert = \\lVert \\sqrt{(3t^2)^2 + (6t)^2 + 6^2} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{9t^4 + 36t^2 + 36} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{9(t^4 + 4t^2 + 4)} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{9((t^2 + 2)^2)} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\pm3(t^2 + 2) \\rVert$<br>\n",
    "$\\qquad\\qquad = 3(t^2 + 2)$\n",
    "\n",
    "Hence, speed $= 3(t^2 + 2)$\n",
    "\n",
    "Next, for acceleration, again:\n",
    "\n",
    "$\\frac{d}{dx}3x^2 = 3 \\frac{d}{dt}t^2 = 6t\\quad, \\frac{d}{dt}6t =6\\quad$, and $\\frac{d}{dt}6 =0$\n",
    "\n",
    "Therefore, acceleration $\\alpha''(t) = (6t, 6, 0)$\n",
    "\n",
    "<b>Solution(b)</b>\n",
    "\n",
    "We know that, arclength$ = \\int_a^b v(t) dt$\n",
    "\n",
    "Here, then it would be:<br>\n",
    "arclength$ = \\int_0^4 (3(t^2 + 2))dt$\n",
    "\n",
    "$\\qquad\\quad = \\int_0^4 (3t^2 + 6) dt$\n",
    "\n",
    "$\\qquad\\quad = \\int_0^4 3t^2 dt + \\int 6 dt$\n",
    "\n",
    "$\\qquad\\quad = 3\\cdot \\frac{t^{2+1}}{2+1} +C + 6t + C$\n",
    "\n",
    "$\\qquad\\quad = 3\\cdot \\frac{t^3}{3} +C + 6t + C$\n",
    "\n",
    "$\\qquad\\quad = t^3 + 6t + C$\n",
    "\n",
    "Now with anitiderivative from $t = 0$  to $t =4$, we have:\n",
    "\n",
    "$[t^3 + 6t + C]_0^4$\n",
    "\n",
    "$= (4^3 + 6\\cdot 4 + C) - (0^3 + 6 \\cdot 0 + C)$\n",
    "\n",
    "$= 64 + 24 + C - 0 - 0 - C$<br>\n",
    "$= 88$\n",
    "\n",
    "Hence, arclength $= 88$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77e1c579",
   "metadata": {},
   "source": [
    "<b>2.2</b><br>\n",
    "Let $\\alpha(t) = (\\frac{1}{2}t^2, 2t, \\frac{4}{3}t^{3/2})$\n",
    "\n",
    "<b>(a)</b> Find the velocity, speed, and acceleration<br>\n",
    "<b>(b)</b> Find the arclength from $t = 2$ to $t = 4$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3649f5d6-6355-46d8-ae3d-9d3296c9a8ed",
   "metadata": {},
   "source": [
    "We know that, <br>\n",
    "<b>Velocity : $ V(t) = \\alpha'(t)$</b> | <b>Acceleration : $\\alpha(t) = \\alpha''(t)$</b> | <b>Speed : $v(t) = \\lVert V(t) \\rVert $</b> | \n",
    "<b>arclength : $ = \\int_a^b v(t)\\,dt$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e5656c1-ac35-46f0-9604-a0e67f611ba6",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b>\n",
    "\n",
    "Here, <br>\n",
    "$\\frac{d}{dt} (\\frac{1}{2}t^2) = \\frac{1}{2}\\cdot \\frac{d}{dt}t^2 = \\frac{1}{2}\\cdot 2t = t$\n",
    "\n",
    "$\\frac{d}{dt}( 2t) = 2 \\cdot \\frac{d}{dt} t = 2$\n",
    "\n",
    "$\\frac{d}{dt} (\\frac{4}{3})(t^{3/2}) = \\frac{4}{3}\\cdot \\frac{3}{2} \\cdot\\frac{d}{dt} t^{3/2 -1} = 2 t^{1/2}$\n",
    "\n",
    "Therefore, velocity, $V(t) = \\alpha'(t) = (t, 2, 2t^{1/2})$\n",
    "\n",
    "Again,<br> \n",
    "$\\frac{d}{dt} t = 1$, $\\qquad \\frac{d}{dt} 2 = 0$ $\\qquad$ and $\\frac{d}{dt} (2t^{1/2}) = 2 \\cdot \\frac{1}{2} \\frac{d}{dt} t^{1/2 -1} = t^{-1/2}$\n",
    "\n",
    "Therefore, acceleration, $\\alpha''(t) = (1, 0, t^{-1/2})$ \n",
    "\n",
    "Next, we have speed, $v(t) = \\lVert V(t) \\rVert$ where  $V(t) = (t, 2, 2t^{1/2})$\n",
    "\n",
    "$\\Rightarrow v(t) = \\lVert \\sqrt{(t)^2 + (2)^2 + (2t^{1/2})^2} \\rVert$\n",
    "\n",
    "$\\qquad\\quad = \\lVert \\sqrt{t^2 + 4 + 4t} \\rVert$\n",
    "\n",
    "$\\qquad\\quad = \\lVert \\sqrt{(t+2)^2} \\rVert$\n",
    "\n",
    "$\\qquad\\quad = t+2 $\n",
    "\n",
    "Hence, speed, $v(t) = t+2$\n",
    "\n",
    "<b>Solution (b)</b>\n",
    "\n",
    "We know that, arclength$ = \\int_a^b v(t) dt$ \n",
    "\n",
    "\n",
    "Here, it would be: <br>\n",
    "$\\int_2^4 (t + 2t) dt$\n",
    "\n",
    "$ = \\int_2^4 t dt + \\int_2^4 2\\cdot dt$\n",
    "\n",
    "$= \\int_2^4 \\frac{t^2}{2} + C + 2t + C$\n",
    "\n",
    "$ = \\int_2^4 \\frac{t^2}{2} + 2t + C$\n",
    "\n",
    "With antiderivative from $t = 2$ to $t = 4$, we can write it as:\n",
    "\n",
    "$[\\frac{t^2}{2} + 2t + C]_2^4$\n",
    "\n",
    "$ = (\\frac{4^2}{2} + 2 \\times 4 + C) - (\\frac{2^2}{2} + 2 \\times 2 + C)$<br>\n",
    "$ = (8 + 8 + C) - (2 + 4 + C)$<br>\n",
    "$ = 16- 6$<br>\n",
    "$ = 10$\n",
    "\n",
    "Hence, arclength$ = 10$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40e3b925",
   "metadata": {},
   "source": [
    "<b>2.3</b><br>\n",
    "\n",
    "Let $\\alpha(t) = (cos 2t, sin 2t, 4t^{3/2})$\n",
    "\n",
    "<b>(a)</b> Find the velocity, speed, and acceleration<br>\n",
    "<b>(b)</b> Find the arclength from $t = 1$ to $t = 2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "757ce91a-cddd-40c6-9e96-ddbb8469527e",
   "metadata": {},
   "source": [
    "We know that, <br>\n",
    "<b>Velocity : $ V(t) = \\alpha'(t)$</b> | <b>Acceleration : $\\alpha(t) = \\alpha''(t)$</b> | <b>Speed : $v(t) = \\lVert V(t) \\rVert $</b> | \n",
    "<b>arclength : $ = \\int_a^b v(t)\\,dt$</b>\n",
    "\n",
    "\n",
    "<b>Solution (a)</b>\n",
    "\n",
    "Here,<br>\n",
    "$\\frac{d}{dt} cos\\,2t = \\frac{d}{du} cos u \\cdot \\frac{du}{dt} 2t$<br>\n",
    "$\\qquad = - sin u \\cdot 2$<br>\n",
    "$\\qquad = -2 sin\\,2t$\n",
    "\n",
    "$\\frac{d}{dt}sin\\,2t = \\frac{d}{dt}sin\\,u \\cdot \\frac{du}{dt}2t$<br>\n",
    "$\\qquad = cos\\,u \\cdot 2$<br>\n",
    "$\\qquad = 2 cos\\,2t$\n",
    "\n",
    "$\\frac{d}{dt} 4t^{3/2} = 4 \\times \\frac{3}{2} \\frac{d}{dt} t^{3/2 -1}$<br>\n",
    "$\\qquad = 6 t^{1/2}$\n",
    "\n",
    "Therefore, velocity, $V(t) = \\alpha'(t) = (-2sin\\,2t, 2cos\\,2t, 6t^{1/2})$\n",
    "\n",
    "Again, <br>\n",
    "$\\frac{d}{dt} (-2sin\\,2t) = -2 \\cdot \\frac{d}{dt}sin\\,u \\frac{d}{dt}2t$<br>\n",
    "$\\qquad = -2 cos\\,u\\cdot 2$<br>\n",
    "$\\qquad = -4 cos\\,2t$\n",
    "\n",
    "$\\frac{d}{dt} 2cos\\,2t = 2 \\cdot \\frac{d}{du} cos\\,u \\cdot \\frac{du}{dt} 2t$<br>\n",
    "$\\qquad = 2 (- sin\\,u) \\cdot 2$<br>\n",
    "$\\qquad = -4 sin\\,2t$\n",
    "\n",
    "$\\frac{d}{dt} 6t^{1/2} = 6 \\times \\frac{1}{2} \\frac{d}{dt}t^{1/2 -1}$<br>\n",
    "$\\qquad = 3t^{-1/2}$\n",
    "\n",
    "Therefore, acceleration, $\\alpha''(t) = (-4cos\\,2t, -4sin\\,2t, 3t^{-1/2})$\n",
    "\n",
    "Next, we need to solve for speed i.e., $v(t) = \\lVert V(t) \\rVert $\n",
    "\n",
    "$\\Rightarrow v(t) = \\lVert \\sqrt{(-2sin\\,2t)^2 + (2cos\\,2t)^2 + (6t^{1/2})^2} \\rVert$<br>\n",
    "$\\qquad\\quad = \\lVert \\sqrt{4sin^2t + 4cos^2 \\,2t + 36t} \\rVert$<br>\n",
    "$\\qquad\\quad = \\lVert \\sqrt{4(sin^2t + cos^2\\,2t) + 36t} \\rVert$<br>\n",
    "$\\qquad\\quad = \\lVert \\sqrt{4 + 36t} \\rVert$<br>\n",
    "$\\qquad\\quad = \\lVert \\sqrt{4 (1 + 9t)} \\rVert$<br>\n",
    "$\\qquad\\quad = 2 \\sqrt{1 + 9t}$<br>\n",
    "\n",
    "Therefore, speed $v(t) = 2 \\sqrt{1 + 9t}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dc992b5-adaf-4d53-bf85-000fea7c574a",
   "metadata": {},
   "source": [
    "<b>Solution (b)</b>\n",
    "\n",
    "Next, for arclength $\\int_a^b v(t) dt$. \n",
    "\n",
    "Here, it would be $\\int_1^2 2(1 + 9t)^{1/2} dt \\qquad\\qquad\\qquad ...eq(1)$\n",
    "\n",
    "Lets say $(1 + 9t = u)$, <br>\n",
    "\n",
    "then, $\\frac{du}{dt} = \\frac{d}{dt} (1 + 9t) = 9$\n",
    "\n",
    "$\\Rightarrow dt = \\frac{du}{9}$\n",
    "\n",
    "Now, we can write $eq(1)$ as: <br>\n",
    "\n",
    "$\\int_1^2 2u^{1/2} \\cdot \\frac{du}{9}$<br>\n",
    "\n",
    "$= \\frac{2}{9} \\int_1^2 u^{1/2} du$\n",
    "\n",
    "$= \\frac{2}{9} \\frac{u^{3/2}}{3/2} = \\frac{2}{9} \\times \\frac{2}{3} u^{3/2} = \\frac{4}{27}u^{3/2}$\n",
    "\n",
    "Subsituting value of $u$ back, we get: $\\quad \\frac{4}{27}(1 + 9t)^{3/2}$\n",
    "\n",
    "With antiderivative from $t = 1$ to $t = 2$, we can write it as:<br>\n",
    "\n",
    "$\\frac{4}{27}(1 + 9\\times 2)^{3/2} - \\frac{4}{27}(1 + 9 \\times 1)^{3/2}$\n",
    "\n",
    "or, $\\frac{4}{27}(19^{3/2} - 10^{3/2})$\n",
    "\n",
    "or, $\\frac{4}{27}(19\\sqrt{19} - 10\\sqrt{10})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f031012",
   "metadata": {},
   "source": [
    "<b>2.4</b><br>\n",
    "\n",
    "Let $a$ and $b$ be real numbers $a \\gt 0$ and let $\\alpha(t) = (a cos\\,t, a sin\\,t, bt)$\n",
    "\n",
    "\n",
    "<b>(a)</b> Find the velocity, speed, and acceleration<br>\n",
    "<b>(b)</b> Find the arclength from $t = 0$ to $t = 2\\pi$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "709538de-4bd7-48c3-a41a-5c8e1aa7cb1b",
   "metadata": {},
   "source": [
    "We know that, <br>\n",
    "<b>Velocity : $ V(t) = \\alpha'(t)$</b> | <b>Acceleration : $\\alpha(t) = \\alpha''(t)$</b> | <b>Speed : $v(t) = \\lVert V(t) \\rVert $</b> | \n",
    "<b>arclength : $ = \\int_a^b v(t)\\,dt$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04375dae-a2de-4157-a212-206f9e8914cf",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b>\n",
    "\n",
    "Here, <br>\n",
    "$\\frac{d}{dt}(a cos\\,t) = a\\cdot \\frac{d}{dt}cos\\,t = -a sin\\,t$<br>\n",
    "\n",
    "$\\frac{d}{dt}sin\\,t = a\\cdot \\frac{d}{dt}sin\\,t = a cos\\,t$\n",
    "\n",
    "$\\frac{d}{dt} bt = b\\cdot \\frac{d}{dt}t = b$\n",
    "\n",
    "Hence, velocity, $V(t) = (-a\\,sin\\,t, a\\,cos\\,t, b)$\n",
    "\n",
    "Again, <br>\n",
    "$\\frac{d}{dt}(-a \\cdot sin\\,t) = -a\\,cos\\,t$\n",
    "\n",
    "$\\frac{d}{dt} acos\\,t = a\\frac{d}{dt}cos\\,t = -a\\,sin\\,t$\n",
    "\n",
    "$\\frac{d}{dt} b = 0$\n",
    "\n",
    "Therefore, acceleration, $\\alpha''(t) = (-acos\\,t, -a\\,sin\\,t, 0)$\n",
    "\n",
    "Now, speed $v(t) = \\lVert V(t) \\rVert$\n",
    "\n",
    "$\\lVert \\sqrt{(-a sin\\,t)^2 + (a cos\\,t)^2 + b^2} \\rVert$\n",
    "\n",
    "$= \\lVert \\sqrt{(a^2 sin^2t + a^2cos^2t + b^2} \\rVert$\n",
    "\n",
    "$= \\lVert \\sqrt{a^2(sin^2t + cos^2t) + b^2} \\rVert$\n",
    "\n",
    "$ = \\lVert \\sqrt{a^2 + b^2} \\rVert$ or $\\sqrt{a^2 + b^2}$\n",
    "\n",
    "Hence, speed $v(t) = \\sqrt{a^2 + b^2}$\n",
    "\n",
    "<b>Solution (b)</b>\n",
    "\n",
    "We know that,  arclength : $\\int_a^b v(t) dt$\n",
    "\n",
    "Here, it would be $\\int_0^{2\\pi} \\sqrt{a^2 + b^2} dt$\n",
    "\n",
    "$\\Rightarrow $ arclength $= \\sqrt{a^2 + b^2} \\int_0^{2\\pi} dt$\n",
    "\n",
    "\n",
    "With antiderivative from $t = 0$ to $t = 2\\pi$, we can write arclength as:\n",
    "\n",
    "arclength$ = [\\sqrt{a^2 + b^2}\\cdot t]_0^{2\\pi}$<br>\n",
    "$\\qquad = \\sqrt{a^2 + b^2}\\cdot 2\\pi - \\sqrt{a^2 - b^2}\\cdot 0$\n",
    "\n",
    "$\\Rightarrow$ arclength$ = 2\\pi \\cdot \\sqrt{a^2 + b^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d59d9a0b",
   "metadata": {},
   "source": [
    "<b>2.5</b>\n",
    "\n",
    "Find a parametrization of the line through the points $a = (1,1,1)$ and $b = (2,3,4)$ that traverses the line with constant speed 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ec8c47f-dfb2-4ab7-a864-4d622b36428e",
   "metadata": {},
   "source": [
    "<b>Solution</b>\n",
    "\n",
    "We can find parametrization of line passing through $a= (1, 1, 1)$ and $b = (2, 3, 4)$ with parametrization:<br>\n",
    "$\\alpha(t) = a + tv$, where $v$ is the direction vector.\n",
    "\n",
    "Here, we can get $v$ as : <br>\n",
    "$v = b - a$<br>\n",
    "$\\Rightarrow v = (2, 3, 4) - (1, 1, 1)$<br>\n",
    "$\\Rightarrow v = (1, 2, 3)$\n",
    "\n",
    "Also, as $v$ traverse the line with constant speed of $1$, we need to normalize $v$ to length $1$.\n",
    "\n",
    "$\\Rightarrow \\hat v = \\frac{v}{\\lVert v \\rVert} = \\frac{(1, 2, 3)}{\\sqrt{1^2 + 2^2 + 3^2}} $\n",
    "\n",
    "$\\Rightarrow \\hat v = \\frac{1}{\\sqrt{14}}(1, 2, 3)$\n",
    "\n",
    "Therefore, parametrization of line would be:<br>\n",
    "\n",
    "$\\alpha(t) = a + t\\hat v$<br>\n",
    "$\\qquad = (1, 1, 1) + t(\\frac{1}{\\sqrt{14}}(1, 2, 3))$\n",
    "\n",
    "$\\Rightarrow$ parametrization : $\\alpha(t) = (1 + \\frac{t}{\\sqrt{14}}, 1 + \\frac{2t}{\\sqrt{14}}, 1 + \\frac{3t}{\\sqrt{14}})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79277c18",
   "metadata": {},
   "source": [
    "----------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c08eb0a",
   "metadata": {},
   "source": [
    "<h3>Section 3: Integrals with respect to arclength</h3>\n",
    "\n",
    "<b>In Exercises 3.1 -3.2, evaluate the integrals with respect to arclength for the curve $C$ with the given parametrization $\\alpha$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "942ff97f",
   "metadata": {},
   "source": [
    "<b>3.1</b> $\\int_C xyz \\, ds$ where $\\alpha(t) = (t^3, 3t^2, 6t), 0 \\le t \\le 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb14c0a1-118f-49cb-8d83-35294e102530",
   "metadata": {},
   "source": [
    "<b>Solution 3.1</b>\n",
    "\n",
    "We know that, <br>\n",
    "\n",
    "Integral of $f$ with respect to arclength, is defined as :<br>\n",
    "$\\int_\\alpha f\\,ds = \\int_a^b f(\\alpha(t))\\,v(t) dt$\n",
    "\n",
    "First, finding speed, $v(t) = \\lVert V(t) \\rVert$\n",
    "\n",
    "Here, we have:<br>\n",
    "$\\frac{d}{dt}t^3  = 3t^2$, $\\qquad \\frac{d}{dt}3t^2 = 6t$, $\\qquad \\frac{d}{dt} = 6$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t)$ or $V(t) = (3t^2, 6t, 6)$\n",
    "\n",
    "Now, $\\lVert V(t) \\rVert = \\lVert \\sqrt{(3t^2)^2 + (6t)^2 + 6^2} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad =  \\lVert \\sqrt{9t^4 + 36t^2 + 36} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad =  \\lVert \\sqrt{9(t^4 + 4t^2 + 4)} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = 3 (t^2 +2) $\n",
    "\n",
    "Also, $\\lVert V(t) \\rVert = \\frac{ds}{dt}$\n",
    "\n",
    "\n",
    "$\\Rightarrow ds = \\lVert V(t) \\rVert dt$<br>\n",
    "$\\Rightarrow ds = 3(t^2 + 2) dt$\n",
    "\n",
    "Now, proceeding with the integrals, we have:\n",
    "\n",
    "$\\int_C xyz \\, ds = \\int_0^1 (t^3)(3t^2)(6t)\\cdot 3(t^2 + 2)dt$\n",
    "\n",
    "$\\qquad\\qquad = \\int_0^1 54t^6(t^2 + 2)dt$\n",
    "\n",
    "$\\qquad\\qquad = 54 \\int_0^1 t^6(t^2 + 2)dt$\n",
    "\n",
    "$\\qquad\\qquad = 54 \\int_0^1 t^8 + 2t^6dt$\n",
    "\n",
    "$\\qquad\\qquad = 54 [ \\int_0^1 t^8 dt +  \\int_0^1 2t^6 dt ]$\n",
    "\n",
    "$\\qquad\\qquad = 54 ( \\frac{t^9}{9} +  \\frac{2t^7}{7})_0^1$\n",
    "\n",
    "$\\qquad\\qquad = 54 ( \\frac{1}{9} +  \\frac{2}{7})$\n",
    "\n",
    "$\\qquad\\qquad = 54 ( \\frac{7 + 18}{63})$\n",
    "\n",
    "$\\qquad\\qquad = 54 \\times \\frac{25}{63}$\n",
    "\n",
    "$\\qquad\\qquad = \\frac{150}{7}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b6af2a",
   "metadata": {},
   "source": [
    "<b>3.2</b> $\\int_c z \\, ds$ where $\\alpha(t) = (cos \\,t + t sin \\, t, sin \\, t - t \\, cos \\, t, t),\\quad 0 \\le t \\le 4$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "113eb911-39e5-4a28-83d9-32907dcb9bd3",
   "metadata": {},
   "source": [
    "<b>Solution 3.2 </b>\n",
    "\n",
    "We know that, <br>\n",
    "\n",
    "Integral of $f$ with respect to arclength, is defined as :<br>\n",
    "$\\int_\\alpha f\\,ds = \\int_a^b f(\\alpha(t))\\,v(t) dt$\n",
    "\n",
    "First, finding speed, $v(t) = \\lVert V(t) \\rVert$\n",
    "\n",
    "Here, we have:<br>\n",
    "$\\frac{d}{dt}(cos\\,t + t\\,sin\\,t) = \\frac{d}{dt}cos\\,t + \\frac{d}{dt} t\\,sin\\,t = (-sin\\,t + t\\,cos\\,t + sin\\,t) = t\\,cos\\,t$\n",
    "\n",
    "$\\frac{d}{dt}(sin\\,t - t\\,cos\\,t) = \\frac{d}{dt}sin\\,t - \\frac{d}{dt} t\\,cos\\,t = cos\\,t  - \\,(-t\\,sin\\,t + cos\\,t) = cos\\,t + tsin\\,t - cos\\,t = t\\,sin\\,t$\n",
    "\n",
    "$\\frac{d}{dt} t = 1$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t) = V(t) = (t\\,cos\\,t, t\\,sin\\,t, 1)$\n",
    "\n",
    "Now, $\\lVert V(t) \\rVert = \\lVert \\sqrt{(t\\,cos\\,t)^2 + (t\\,sin\\,t)^2 + 1^2} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{t^2 cos^2\\,t + t^2 sin^2\\,t + 1}  \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{t^2(cos^2\\,t + sin^2\\,t) +1} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{t^2 + 1}\\rVert$\n",
    "\n",
    "$\\Rightarrow V(t) =\\sqrt{t^2 + 1}$\n",
    "\n",
    "$\\Rightarrow ds = \\sqrt{t^2 +1} \\,dt$\n",
    "\n",
    "Now, proceeding with integral, we have:\n",
    "\n",
    "$\\int_c z \\, ds = \\int_0^4 t\\cdot \\sqrt{t^2 + 1} \\,dt\\qquad\\qquad.....eq(1)$\n",
    "\n",
    "Let $u = t^2 + 1$<br>\n",
    "$\\Rightarrow \\frac{du}{dt} = \\frac{d}{dt}(t^2 + 1) = 2t$<br>\n",
    "$\\Rightarrow du = 2t\\,dt$<br>\n",
    "$\\Rightarrow t.dt = \\frac{du}{2}$\n",
    "\n",
    "Also, when $t = 0$, $u = 0^2 + 1 = 1$<br>\n",
    "and, when $t = 4$, $u = 4^2 + 1 = 17$\n",
    "\n",
    "Now, re-writing $eq(1)$, we get :\n",
    "\n",
    "$\\int_1^{17} \\sqrt{u} \\frac{du}{2}$\n",
    "\n",
    "$ = \\frac{1}{2} \\int_1^{17} u^{1/2} du$\n",
    "\n",
    "$ = \\frac{1}{2} \\cdot \\frac{2}{3} u^{3/2} |_1^{17}$\n",
    "\n",
    "$ = \\frac{1}{3}(17^{3/2} - 1^{3/2})$\n",
    "\n",
    "$ = \\frac{1}{3}(17\\sqrt{17} - 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c368c869",
   "metadata": {},
   "source": [
    "<b>3.3</b> Let $C$ be the line segment in $\\mathbb{R}^2$ from $(1,0)$ to $(0,1)$. With as little calculation as possible, find the values of the following integrals.\n",
    "\n",
    "<b>(a)</b> $\\int_C 5 \\, ds$<br>\n",
    "<b>(b)</b> $\\int_C (x + y) \\, ds$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e546ad8e-7c13-4b4c-9598-3929f02077dd",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b>\n",
    "\n",
    "Length of $C = \\sqrt{(1-0)^2 + (0-1)^2} = \\sqrt{1 + 1} = \\sqrt{2}$\n",
    "\n",
    "and, since function $f$ is constant value $5$, we can get $\\int_C 5 ds = 5 \\times \\sqrt{2} = 5\\sqrt{2}$ \n",
    "\n",
    "<b>Solution (b)</b>\n",
    "\n",
    "The line passes through $(1, 0)$ to $(0,1)$<br>\n",
    "$\\Rightarrow v = b - a = (0,1) - (1,0) = (-1,1)$\n",
    "\n",
    "$\\Rightarrow \\alpha(t) = (1, 0) + t(-1, 1)$<br>\n",
    "$\\Rightarrow \\alpha(t) = (1-t, t)$\n",
    "\n",
    "So, $\\alpha'(t) = (-1,1)$<br>\n",
    "Then, $\\lVert \\alpha'(t) \\rVert  = \\sqrt{(-1)^2 + 1^2} = \\sqrt{2}$\n",
    "\n",
    "Therefore, $\\int_C (x + y) ds$ becomes :\n",
    "\n",
    "$\\int_0^1 ((1-t) + t) \\lVert \\alpha'(t)\\rVert \\,dt \\qquad= \\int_0^1 1 \\cdot \\sqrt{2} \\,dt \\qquad= \\sqrt{2}\\int_0^1 1dt$\n",
    "\n",
    "or, $\\sqrt{2}\\,(t)_0^1 = \\sqrt{2}(1 - 0 ) = \\sqrt{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e059494c",
   "metadata": {},
   "source": [
    "<b>3.4</b> Let $C$ be the line segment in $\\mathbb{R}^2$ parametrized by $\\alpha(t) = (t, t), \\quad 0 \\le t \\le 1$\n",
    "\n",
    "<b>(a)</b> Evaluate $\\int_C (x + y) ds$<br>\n",
    "<b>(b)</b> Find a triangle in $\\mathbb{R}^3$ whose base is the segment $C$ (in th $xy-$plane) and whose area is represented by the integral in part(a). (Hint: Area under curve)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "342ad231-6ec4-488d-bda3-e3fadc03a672",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b>\n",
    "\n",
    "Since, $\\alpha(t) = (t, t)$ and $\\frac{d}{dt}t = 1$, we get:<br>\n",
    "$\\alpha'(t) = (1, 1)$\n",
    "\n",
    "Therefore, $\\lVert \\alpha'(t) \\rVert = \\sqrt{1^2 + 1^2} = \\sqrt{2}$\n",
    "\n",
    "Then $\\int_C (x + y) ds $ becomes :\n",
    "\n",
    "$\\int_0^1 (t + t) \\lVert \\alpha'(t) \\rVert \\,dt \\qquad= \\int_0^1 2t \\sqrt{2} dt \\qquad= 2\\sqrt{2} \\int_0^1 t\\,dt$\n",
    "\n",
    "or, $2\\sqrt{2} \\frac{t^2}{2} |_0^1 \\qquad= \\frac{2\\sqrt{2}}{2} (1^2 - 0^2) = \\sqrt{2}\\cdot 1 = \\sqrt{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a19ab08",
   "metadata": {},
   "source": [
    "---------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fd07b2c",
   "metadata": {},
   "source": [
    "<h3>Section 4: The Geometry of Curves: Tangent and Normal Vectors</h3>\n",
    "\n",
    "<b>In Exercises 4.1-4.2, find the unit tangent $T(t)$ and the principal normal $N(t)$ for the given path $\\alpha$. Then, verify that $T(t)$ and $N(t)$ are orthogonal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c3f8d30",
   "metadata": {},
   "source": [
    "<b>4.1</b> $\\alpha(t) = (sin \\, 4t, cos \\, 4t, 3t)$\n",
    "\n",
    "<b> 4.2</b> $\\alpha(t) = (t, t^2, 0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24b746b9-35b7-47ea-9ad5-26948c1f7b4f",
   "metadata": {},
   "source": [
    "We know that, <br>\n",
    "unit tangent vector, $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert} \\alpha'(t)$ and principal normal $N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4beb197d-224a-4284-921c-c7a1856c27ff",
   "metadata": {},
   "source": [
    "<b>Solution 4.1</b>\n",
    "\n",
    "Here, <br>\n",
    "$\\frac{d}{dt}sin\\,4t = \\frac{d}{du}(sin\\,u) \\frac{d}{dt}4t\\qquad$ where $u = 4t$\n",
    "\n",
    "$\\frac{d}{dt}sin\\,4t = cos\\,u \\cdot 4 = 4 \\,cos\\,4t$\n",
    "\n",
    "Similarly, $\\frac{d}{dt}cos\\,4t = -4\\,sin\\,4t\\qquad$ and $\\frac{d}{dt}3t = 3$\n",
    "\n",
    "Then,$\\alpha'(t) = (4\\,cos\\,4t, -4\\,sin\\,4t, 3)$\n",
    "\n",
    "So, $\\lVert \\alpha'(t) \\rVert = \\lVert \\sqrt{(4\\,cos\\,4t)^2 + (-4\\,sin\\,4t)^2 + 3^2} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{16cos^2\\,4t + 16sin^2\\,4t + 9} \\rVert $\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{16(cos^2\\,4t + sin^2\\,4t) + 9} \\rVert $<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{16+ 9} \\rVert $<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{25} \\rVert $<br>\n",
    "$\\qquad\\qquad = 5 $\n",
    "\n",
    "Therefore, <b>unit tangent vector, $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert} \\alpha'(t) = \\frac{1}{5}(4\\,cos\\,4t, -4\\,sin\\,4t, 3)$</b>\n",
    "\n",
    "Here, $T(t) = (\\frac{4}{5}cos\\,4t, \\frac{-4}{5}sin\\,4t, \\frac{3}{5})$\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{4}{5}cos\\,4t) = \\frac{4}{5}\\frac{d}{dt}cos\\,4t = \\frac{4}{5}(-4\\,sin\\,4t) = -\\frac{16}{5}sin\\,4t$\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{-4}{5}sin\\,4t) = \\frac{-4}{5}\\frac{d}{dt}sin\\,4t = \\frac{-4}{5}(4\\,cos\\,4t) = -\\frac{16}{5}cos\\,4t$\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{3}{5}) = 0$\n",
    "\n",
    "$\\Rightarrow T'(t) = (-\\frac{16}{5}sin\\,4t, -\\frac{16}{5}cos\\,4t, 0)$\n",
    "\n",
    "or, $T'(t) = \\frac{16}{5}(-sin\\,4t, -cos\\,4t, 0)$\n",
    "\n",
    "Now, $\\lVert T'(t) \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{(-\\frac{16}{5}sin\\,4t)^2 + (-\\frac{16}{5}cos\\,4t)^2 + 0^2}\\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{256}{25}(sin^2\\,4t + cos^2\\,4t)}\\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{256}{25}}\\rVert$\n",
    "\n",
    "$\\Rightarrow \\lVert T'(t) \\rVert = \\frac{16}{5}$\n",
    "\n",
    "Since, $N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t)$, we get\n",
    "\n",
    "$N(t) = \\frac{1}{16/5} \\frac{16}{5}(-sin 4t, - cos 4t, 0)$<br>\n",
    "$\\qquad = (-sin 4t, - cos 4t, 0)$\n",
    "\n",
    "Therefore, <b>principal normal, $N(t) = (-sin 4t, - cos 4t, 0)$</b>\n",
    "\n",
    "Next, <br>\n",
    "$T(t) \\cdot N(t) = \\frac{1}{5}(4\\,cos\\,4t, -4\\,sin\\,4t, 3)(-sin 4t, - cos 4t, 0)$<br>\n",
    "$\\Rightarrow T(t) \\cdot N(t) = \\frac{1}{5}(4\\,cos\\,4t(-sin\\,4t), -4\\,sin\\,4t(- cos 4t) + 3\\cdot 0)$<br>\n",
    "$\\Rightarrow T(t) \\cdot N(t) = \\frac{1}{5}(-4\\,cos\\,4t sin\\,4t, + 4sin\\,4t\\,cos\\,4t + 0)$\n",
    "\n",
    "$\\Rightarrow T(t) \\cdot N(t) = 0$\n",
    "\n",
    "Hence, <b>$T(t)$ and $N(t)$ are orthogonal</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abd2db8b-fbcc-4960-8ab3-765e8cb9e55f",
   "metadata": {},
   "source": [
    "<b>Solution 4.2</b>\n",
    "\n",
    "\n",
    "We have, $\\alpha(t) = (t, t^2, 0)$\n",
    "\n",
    "Here, $\\frac{d}{dt}t = 1, \\qquad \\frac{d}{dt}t^2 = 2t, \\qquad \\frac{d}{dt} =0$\n",
    "\n",
    "Therefore, $\\alpha'(t) = (1, 2t,0)$\n",
    "\n",
    "So, $\\lVert \\alpha'(t) \\rVert = \\sqrt{1^2 + (2t)^2 + 0^2}$\n",
    "\n",
    "$\\qquad\\qquad = \\sqrt{1 + 4t^2}$\n",
    "\n",
    "Therefore, <b>unit tangent vector, $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert} \\alpha'(t) = \\frac{1}{\\sqrt{1 + 4t^2}}(1, 2t, 0)$</b>\n",
    "\n",
    "$\\Rightarrow T(t) = (\\frac{1}{\\sqrt{1 + 4t^2}}, \\frac{2t}{\\sqrt{1 + 4t^2}},0)$\n",
    "\n",
    "Here, in the case of $\\frac{1}{\\sqrt{1 + 4t^2}}$ Let $u = 1+4t^2$, then we have, \n",
    "\n",
    "$g(u) = \\frac{1}{\\sqrt{u}}$ and $\\frac{du}{dt} = 8t$\n",
    "\n",
    "Now solving $g(u) = \\frac{1}{\\sqrt{u}}$, <br>\n",
    "$\\qquad g'(u) = \\frac{d}{du}u^{-1/2}$<br>\n",
    "$\\qquad = -\\frac{1}{2}u^{-3/2}$<br>\n",
    "$\\qquad = - \\frac{1}{2u^{3/2}}$\n",
    "\n",
    "Next, $\\frac{d}{dt}(\\frac{1}{\\sqrt{1+t^2}}) = g'(u) \\cdot \\frac{du}{dt}$\n",
    "\n",
    "$\\qquad = - \\frac{1}{2u^{3/2}} \\cdot 8t$\n",
    "\n",
    "$\\qquad = - \\frac{1}{2(1+4t^2)^{3/2}} \\cdot 8t$\n",
    "\n",
    "$\\qquad = - \\frac{4t}{(1+4t^2)^{3/2}}$\n",
    "\n",
    "Next, as per Quotient rule of $(\\frac{f(x)}{g(x)})' = \\frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$\n",
    "\n",
    "if $f(x) = 2t$, then $f'(x) = 2$\n",
    "\n",
    "and, if $g(x) = \\sqrt{1+4t^2}$, then $g'(x) = \\frac{d}{dt} (1 + 4t)^{1/2}$\n",
    "\n",
    "$\\Rightarrow g'(x) = \\frac{1}{2}\\cdot \\frac{1}{\\sqrt{1 + 4t^2}} \\cdot 8t$\n",
    "\n",
    "$\\Rightarrow g'(x) = \\frac{4t}{\\sqrt{1+4t^2}}$\n",
    "\n",
    "Next, $(\\frac{2t}{\\sqrt{1 + 4t^2}})'=\\frac{2 \\sqrt{1 + 4t^2} - (2t\\cdot \\frac{4t}{\\sqrt{1 + 4t^2}})}{\\sqrt{1+4t^2}}$\n",
    "\n",
    "$\\quad = \\frac{\\frac{2 \\sqrt{1+4t^2}\\sqrt{1+4t^2} -8t^2}{\\sqrt{1+4t^2}}}{(\\sqrt{1+4t^2})^2}$\n",
    "\n",
    "$\\quad = \\frac{\\frac{2 (1+4t^2) -8t^2}{\\sqrt{1+4t^2}}}{{1+4t^2}}$\n",
    "\n",
    "$\\quad = \\frac{\\frac{2+ 8t^2 -8t^2}{\\sqrt{1+4t^2}}}{{1+4t^2}}$\n",
    "\n",
    "$\\quad = \\frac{2}{(1+4t^2)\\sqrt{1+4t^2}}$\n",
    "\n",
    "$T'(t) = (- \\frac{4t}{(1+4t^2)^{3/2}}, \\frac{2}{(1+4t^2)\\sqrt{1+4t^2}}, 0)$\n",
    "\n",
    "Now, $\\lVert T'(t) \\rVert = \\lVert \\sqrt{(- \\frac{4t}{(1+4t^2)^{3/2}})^2 + (\\frac{2}{(1+4t^2)\\sqrt{1+4t^2}})^2 + 0} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{16t^2}{(1+4t^3)} + \\frac{4}{(1+4t^2)^2(1+4t)} + 0} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{16t^2}{(1+4t^2)^3} + \\frac{4}{(1+4t^2)^3} + 0} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{4 + 16t^2}{(1+4t^2)^3}} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{4(1 + 4t^2)}{(1+4t^2)^3}} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{4}{(1+4t^2)^2}} \\rVert$\n",
    "\n",
    "$\\qquad \\lVert T'(t) \\rVert = \\frac{2}{(1+4t^2)}$\n",
    "\n",
    "Then, <br>\n",
    "\n",
    "$N(t) = \\frac{1}{\\lVert T'(t) \\rVert} T'(t)$\n",
    "\n",
    "$\\Rightarrow N(t) = \\frac{1}{\\frac{2}{(1+4t^2)}} (- \\frac{4t}{(1+4t^2)^{3/2}}, \\frac{2}{(1+4t^2)\\sqrt{1+4t^2}}, 0)$\n",
    "\n",
    "$\\Rightarrow N(t) = (- \\frac{4t}{(1+4t^2)^{3/2}} \\cdot \\frac{(1+4t^2)}{2}, \\frac{2}{(1+4t^2)\\sqrt{1+4t^2}} \\cdot \\frac{(1+4t^2)}{2}, 0)$\n",
    "\n",
    "$\\Rightarrow$ <b>Principal Normal, N(t)</b>$ = (- \\frac{2t}{(1+4t^2)^{1/2}}, \\frac{1}{(1+4t^2)^{1/2}}, 0)$\n",
    "\n",
    "Next, <br>\n",
    "$T(t) \\cdot N(t) = (\\frac{1}{(1+4t^2)^{1/2}}, \\frac{2t}{(1+4t^2)^{1/2}},0) \\cdot (- \\frac{2t}{(1+4t^2)^{1/2}}, \\frac{1}{(1+4t^2)^{1/2}}, 0)$\n",
    "\n",
    "$\\Rightarrow T(t) \\cdot N(t) = \\frac{1}{(1+4t^2)^{1/2}}\\cdot\\frac{-2t}{(1+4t^2)^{1/2}} + \\frac{2t}{(1+4t^2)^{1/2}} \\cdot \\frac{1}{(1+4t^2)^{1/2}} + 0$ \n",
    "\n",
    "$\\Rightarrow T(t) \\cdot N(t) = 0$\n",
    "\n",
    "Hence, <b>$T(t)$ and $N(t)$ are orthonormal</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d690c44",
   "metadata": {},
   "source": [
    "<b>4.3</b> Let $\\alpha$ be a differentiable path in $\\mathbb{R}^n$\n",
    "\n",
    "<b>(a)</b> If the speed is constant, show that the velocity and acceleration vectors are always orthogonal (Hint: Consider $\\lVert v(t) \\rVert^2$)\n",
    "\n",
    "<b>(b)</b> Conversely, if the velocity and acceleration are orthogonal, show that the speed is constant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f95496c-826d-403c-8657-bb5354ab7937",
   "metadata": {},
   "source": [
    "<b> Solution 4.3(a)</b>\n",
    "\n",
    "We know that, <br>\n",
    "Two vector, $u$ and $v$ are orthogonal when $u \\cdot v = 0$,<br>\n",
    "and, acceleration vector $a(t) = \\frac{d}{dt}V(t)$\n",
    "\n",
    "We have, speed as constant, so lets take it as $C = \\lVert V(t) \\rVert$ for all $t$\n",
    "\n",
    "Now, take square of speed as :\n",
    "\n",
    "$ \\lVert V(t) \\rVert = C^2$\n",
    "\n",
    "and differentiate w.r.t $t$<br>\n",
    "$\\Rightarrow \\frac{d}{dt}  \\lVert V(t) \\rVert^2 = \\frac{d}{dt} C^2$\n",
    "\n",
    "Since, $C$ is constant, we get: <br>\n",
    "\n",
    "$\\Rightarrow \\frac{d}{dt}  \\lVert V(t) \\rVert^2 = 0$\n",
    "\n",
    "$\\Rightarrow 2 V(t) \\frac{d}{dt}V(t) = 0$\n",
    "\n",
    "$\\Rightarrow 2 V(t) \\cdot a(t) = 0$\n",
    "\n",
    "$\\Rightarrow V(t) \\cdot a(t) = 0$<br>\n",
    "Thus, we can say that when speed $C$ is constant, velocity, $V(t)$ and aceleration $a(t)$ are orthogonal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f17a274e-0aa8-44be-af86-d7ff40111d66",
   "metadata": {},
   "source": [
    "<b>Solution 4.3(b)</b>\n",
    "\n",
    "We are given, velocity $V(t)$ and acceleration $a(t)$ are orthogonal.<br>\n",
    "$\\Rightarrow V(t) \\cdot a(t) = 0$\n",
    "\n",
    "and, we know that acceleration, $a(t) = \\frac{d}{dt}V(t)$\n",
    "\n",
    "Now, lets take square od speed $\\lVert V(t) \\rVert ^2$ and differentiate it w.r.t $t$, we get:\n",
    "\n",
    "$\\frac{d}{dt} \\lVert V(t) \\rVert ^2= 2 \\cdot V(t) \\frac{d}{dt} V(t)$\n",
    "\n",
    "$\\qquad\\qquad = 2 V(t) \\cdot a(t)$ <br>\n",
    "$\\qquad\\qquad = 0$ \n",
    "\n",
    "$\\Rightarrow$ square of speed,$\\lVert V(t) \\rVert ^2$, is constant\n",
    "\n",
    "Therefore, speed must also be constant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5908c750",
   "metadata": {},
   "source": [
    "<b>4.4</b> Let $C$ be a curve in $\\mathbb{R}^n$ traced out by a differentiable path $\\alpha : (a, b) \\to \\mathbb{R}^n$ defined on an open interval $(a, b)$. Assume that there is a point $\\alpha(t_0)$ on $C$ that is closer to the origin than any other point of $C$. Prove that the tangent vector $\\alpha'(t_0)$ is orthogonal to $\\alpha(t_0)$. Draw a sketch that illustrates the conclusion."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8d6918a-7202-45dc-a296-781280e43885",
   "metadata": {},
   "source": [
    "<b>Solution 4.4</b>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a3e2431",
   "metadata": {},
   "source": [
    "-----------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbd131eb",
   "metadata": {},
   "source": [
    "<h3> Section 5: The cross product </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d40df3f2",
   "metadata": {},
   "source": [
    "<b> In Exercise 5.1 - 5.4 (a) find the cross product $v \\times w$ and (b) verify that it is orthogonal to $v$ and $w$</b>\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6710367a",
   "metadata": {},
   "source": [
    "<b>5.1</b> $v = (1, 1, 1), w = (1, 3, 5)$<br>\n",
    "<b>5.2</b> $v = (1, 2, 3), w = (2, 4, 6)$<br>\n",
    "<b>5.3</b> $v = (1, -2, 4), w = (-2, 1, 3)$<br>\n",
    "<b>5.4</b> $v = (2, 0, -1), w = (0, -2, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac4dcc47-8bff-4e69-aebc-63d6091a2768",
   "metadata": {},
   "source": [
    "<b>Solution 5.1</b><br>\n",
    "\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "1&1&1\\\\\n",
    "1&3&5\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(1(5) -3(1))i - (1(5) - 1(1))j + (1(3) - 1(1))k]$<br>\n",
    "$\\quad = 2i - 4j + 2k$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w = (2, -4, 2)$\n",
    "\n",
    "Here, $v \\cdot (v \\times w) = (1,1,1)(2, -4, 2) = 1(2) + 1(-4) + 1(2) = 2 -4 -2 = 0$<br>\n",
    "and, $w \\cdot (v \\times w) = (1, 3, 5)(2, -4, 2) = 1(2) +3(-4) + 5(2) = 2 -12 + 10 = 0$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w$ is orthogonal to $v$ and $w$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb823f64-01ca-440c-9755-0f800290c7a2",
   "metadata": {},
   "source": [
    "<b>Solution 5.2</b> <br>\n",
    "\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "1&2&3\\\\\n",
    "2&4&6\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(2(6) -3(4))i - (1(6) - 2(3))j + (1(4) - 2(2))k]$<br>\n",
    "$\\quad = 0i - 0j + 0k$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w = (0, 0, 0)$\n",
    "\n",
    "Here, $v \\cdot (v \\times w) = (1,1,1)(0, 0, 0) = 1(0) + 1(0) + 1(0)  = 0$<br>\n",
    "and, $w \\cdot (v \\times w) = (1, 3, 5)(0, 0, 0) = 1(0) +3(0) + 5(0)  = 0$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w$ is orthogonal to $v$ and $w$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4903df1-b8cc-4492-ab73-9fdffe127a25",
   "metadata": {},
   "source": [
    "<b> Solution 5.3 </b>\n",
    "\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "1&-2&4\\\\\n",
    "-2&1&3\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(-2(3) -1(4))i - (1(3) - (-2)(4))j + (1(1) - (-2)(-2))k]$<br>\n",
    "$\\quad = -10i - 11j -3k$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w = (-10, -11, -3)$\n",
    "\n",
    "Here, $v \\cdot (v \\times w) = (1,-2,1)(-10, -11, -3) = 1(-10) + -2(-11) + 4(-3) = -10 + 22 - 12 = 0$<br>\n",
    "and, $w \\cdot (v \\times w) = (-2, 1, 3)(-10, -11, -3) = -2(-10) +1(-11) + 3(-3) = 20 -11 -9  = 0$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w$ is orthogonal to $v$ and $w$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8d163f0-9932-442b-942f-1d841e20456c",
   "metadata": {},
   "source": [
    "<b>Solution </b><br>\n",
    "\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "2&0&-1\\\\\n",
    "0&-2&1\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(0(1) -(-2)(-1))i - (2(1) - (0)(-1))j + (2(2) - (0)(0))k]$<br>\n",
    "$\\quad = -2i - 2j +4k$<br>\n",
    "\n",
    "$\\Rightarrow v \\times w = (-2, -2, 4)$\n",
    "\n",
    "Here, $v \\cdot (v \\times w) = (-2, -2, 4)(2, 0, 1) = -4 + 0 + 4 = 0$<br>\n",
    "and $w \\cdot (v \\times w) = (-2, -2, 4)(0, -2, 1) = 0 -4 + 4 = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "252307ab-f541-40eb-9206-8918537e7799",
   "metadata": {},
   "source": [
    "<b> 5.5 </b> Find a non-zero vector in $\\mathbb{R}^3$ that points in a direction perpendicular to the plane that contains the origin and the points $p = (1, 1, 1)$ and $q = (2, 1, -3)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64cbaf9-83d2-4be4-b5eb-be24722709af",
   "metadata": {},
   "source": [
    "<b> Solution 5.5 </b>\n",
    "\n",
    "We can get it by cross-product. Here, <br>\n",
    "\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "1&1&1\\\\\n",
    "2&1&-3\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(1(-3) -1(1))i -j(1(-3) -2(1)) +k(1(1) -2(1))]$<br>\n",
    "$\\quad = -4i + 5j -1k$<br>\n",
    "\n",
    "Hence, the non-zero vector would be $(-4, 5, -1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba039970-4bb2-4d1a-87e6-8fd6d61bd540",
   "metadata": {},
   "source": [
    "<b> 5.6</b> Find a non-zero vector in $\\mathbb{R}^3$ that points in a direction to the plane that contains the points $p = (1, 0,0), q = (0,1,0)$ and $r = (0,0,1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19b7bf3e-5c6b-49bb-ae78-cfc6d779671e",
   "metadata": {},
   "source": [
    "<b>Solution 5.6</b> <br>\n",
    "\n",
    "we can use again the cross-product of the two vector lying in the direction to get the required vector.\n",
    "\n",
    "Here, $\\overrightarrow pq = q - p  = (0,1,0) - (1,0,0) = (-1,1,0)$<br>\n",
    "and, $\\overrightarrow pr = r -p = (0,0,1) - (1,0,0) = (-1,0,1)$\n",
    "\n",
    "Now, the cross-product of $pq \\times pr = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "-1&1&0\\\\\n",
    "-1&0&1\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(1(1) - 0(0))i - ((-1)1 - (-1)0)j +((-1)0 - (-1)1)k]$<br>\n",
    "$\\quad = 1i -1j +1k$<br>\n",
    "\n",
    "Hence, the required vector is $(1, -1, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0888ec3d",
   "metadata": {},
   "source": [
    "<b>5.7</b> Let $v = (-1,1,-2), w = (4, -1, -1)$ and $u = (-3,2,1)$<br>\n",
    "\n",
    "<b>(a)</b> Find $v \\times w$<br>\n",
    "<b>(b)</b> What is the area of the parallelogram determined by $v$ and $w$<br>\n",
    "<b>(c)</b> Find $u \\cdot (v \\times w)$. Then, use your answer to find $v \\cdot (u \\times w)$ and $(u \\times v) \\cdot w$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42065bdf-4aa8-4f0f-89e6-66a288b7e21f",
   "metadata": {},
   "source": [
    "<b>Solution 5.7 (a)</b> <br>\n",
    "\n",
    "Here, $v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "-1&1&-2\\\\\n",
    "4&-1&-1\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\quad = [(1(-1) - (-1)(-2)i - (-1(-1) -4(-2))j + ((-1)(-1) -4(1))k]$<br>\n",
    "$\\quad = (-1-2)i - (1+8)j + (1-4)k) = -3i - 9j -3k$\n",
    "\n",
    "Hence, $v \\times w = (-3, -9, -3)$\n",
    "\n",
    "<b>Solution 5.7(b)</b>\n",
    "\n",
    "We know that, area of parallelogram = base $\\times$ height $= \\lVert v \\rVert (\\lVert w\\rVert sin \\theta)$<br>\n",
    "or $\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad = \\lVert v \\times w \\rVert$\n",
    "\n",
    "Then, it woud be $\\sqrt{(-3)^2 + (-9)^2 + (-3)^2}$<br>\n",
    "or, $\\qquad\\qquad = \\sqrt{9 + 81 + 9}$<br>\n",
    "or, $\\qquad\\qquad = \\sqrt{99}$\n",
    "\n",
    "\n",
    "$\\Rightarrow$ area of parallelogram $= 3\\sqrt{11}$<br>\n",
    "\n",
    "<b>Solution 5.7(c)</b>\n",
    "\n",
    "We have, $v \\times w = (-3, -9, -3)$<br>\n",
    "Therfore, $u \\cdot (v \\times w) = (-3, 2, 1)\\cdot (-3, -9, -3) = 9 - 18 -3$<br>\n",
    "$\\Rightarrow u \\cdot (v \\times w) = -12$\n",
    "\n",
    "We know that,<br>\n",
    "$v \\cdot (u \\times w) = det[v\\quad u\\quad w]$<br>\n",
    "By row switching, we can write it as:<br>\n",
    "$v \\cdot (u \\times w) = - det[u\\quad v\\quad w]$<br>\n",
    "\n",
    "$\\Rightarrow v \\cdot (u \\times w) = - u \\cdot (v \\times w) = - (- 12)$<br>\n",
    "$\\Rightarrow v \\cdot (u \\times w) = 12$<br>\n",
    "\n",
    "\n",
    "Again, <br>\n",
    "$(u \\times v) \\cdot w = det[u \\quad v \\quad w]$<br>\n",
    "$\\qquad \\qquad\\quad = u \\cdot (v \\times w)$<br>\n",
    "$\\qquad \\qquad\\quad = -12$<br>\n",
    "$\\Rightarrow (u \\times v) \\cdot w = -12$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b7c57cd",
   "metadata": {},
   "source": [
    "<b> 5.8</b> Verify that the cross product $v \\times w$ as defined in equation (x) satisfies the key property that $x \\cdot (v \\times w) = det[x\\, v \\,w]$ for all $x$ in $\\mathbb{R}^3$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3522b1a-9a15-4648-b355-ca7552edc7ed",
   "metadata": {},
   "source": [
    "<b>Solution 5.8</b> <br>\n",
    "equation (x) states if $v = (v_1, v_2, v_3)$ and $w = (w_1, w_2, w_3)$ then,\n",
    "\n",
    "$\\qquad\\qquad v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "v_1&v_2&v_3\\\\\n",
    "w_1&w_2&w_3\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\qquad\\qquad\\qquad = (v_2w_3 - v_3w_2)i - (v_1w_3 - v_3w_1)j + (v_1w_2 - v_2w_1)k$\n",
    "\n",
    "Then, if $x = (x_1, x_2, x_3)$<br>\n",
    "$x \\cdot (v \\times w) = (x_1, x_2, x_3)((v_2w_3 - v_3w_2)i - (v_1w_3 - v_3w_1)j + (v_1w_2 - v_2w_1)k)$\n",
    "\n",
    "$\\qquad\\qquad = (v_2w_3 - v_3w_2)x_1 - (v_1w_3 - v_3w_1)x_2 + (v_1w_2 - v_2w_1)x_3$\n",
    "\n",
    "Next, <br>\n",
    "$det[x\\quad v \\quad w] = \\begin{vmatrix}\n",
    "x_1 & x_2 &x_3\\\\\n",
    "v_1 & v_2&v_3\\\\\n",
    "w_1&w_2&w_3\\\\\n",
    "\\end{vmatrix}$\n",
    "\n",
    "$\\qquad\\qquad\\qquad = (v_2w_3 - v_3w_2)x_1 - (v_1w_3 - v_3w_1)x_2 + (v_1w_2 - v_2w_1)x_3$\n",
    "\n",
    "Hence, proved!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b19968b",
   "metadata": {},
   "source": [
    "<b>5.9</b> Let $v = (v_1, v_2, v_3)$ and $w = (w_1, w_2, w_3)$ be vectors in $\\mathbb{R}^3$\n",
    "\n",
    "<b>(a)</b> Use the definitions of the dot and cross products in terms of coordinates to prove that:\n",
    "\n",
    "$$\\lVert v \\times w \\rVert^2 = \\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2$$\n",
    "\n",
    "<b>(b)</b> Use part(a) to give a proof that $\\lVert v \\times w \\rVert = \\lVert v \\rVert \\lVert w \\rVert sin \\theta $, where $\\theta$ is the angle between $v$ and $w$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "399ef077-3911-49f7-9e4e-86769bad6f2e",
   "metadata": {},
   "source": [
    "<b>Solution 5.9 (a)</b>\n",
    "\n",
    "We know that, <br>\n",
    "$v \\times w = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "v_1&v_2&v_3\\\\\n",
    "w_1&w_2&w_3\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\qquad\\qquad\\qquad = (v_2w_3 - v_3w_2)i - (v_1w_3 - v_3w_1)j + (v_1w_2 - v_2w_1)k$<br>\n",
    "$\\qquad\\qquad\\qquad = \\left((v_2w_3 - v_3w_2), (v_1w_3 - v_3w_1), (v_1w_2 - v_2w_1)\\right)$\n",
    "\n",
    "<b>$\\Rightarrow \\lVert v \\times w \\rVert^2 = (v_2w_3 - v_3w_2)^2 +  (v_1w_3 - v_3w_1)^2 + (v_1w_2 - v_2w_1)^2$</b>\n",
    "\n",
    "$= (v_2^2w_3^2 + v_3^2w_2^2 - 2v_2w_3v_3w_2) + (v_1^2w_3^2 + v_3^2w_1^2 - 2v_1w_3v_3w_1) + (v_1^2w_2^2 + v_2^2w_1^2 - 2v_1w_2v_2w_1)$\n",
    "\n",
    "$\\Rightarrow \\lVert v \\times w \\rVert^2 = v_1^2w_2^2 + v_1^2w_3^2 + v_2^2w_1^2 + v_2^2w_3^2 + v_3^2w_1^2 + v_3^2w_2^2  - 2v_1w_1v_2w_2 - 2v_2w_2v_3w_3 - 2v_1w_1v_3w_3\\qquad\\qquad \\qquad ...eq(1)$\n",
    "\n",
    "Similarly,\n",
    "\n",
    "\n",
    "$\\lVert v \\rVert^2  = (v_1^2 + v_2^2 + v_3^2)$<br>\n",
    "$\\lVert w \\rVert^2  = (w_1^2 + w_2^2 + w_3^2)$\n",
    "\n",
    "and, $v \\cdot w = (v_1, v_2, v_3)\\cdot (w_1, w_2, w_3)$<br>\n",
    "\n",
    "$\\qquad\\qquad = v_1w_1 + v_2w_2 + v_3w_3$\n",
    "\n",
    "$\\Rightarrow (v \\cdot w)^2 = (v_1w_1 + v_2w_2 + v_3w_3)^2$<br>\n",
    "$\\qquad\\qquad = v_1^2w_1^2 + v_2^2w_2^2 + v_3^2w_3^2 + 2v_1w_1v_2w_2 + 2v_2w_2v_3w_3 + 2v_1w_1v_3w_3$\n",
    "\n",
    "Next in the RHS of the equation, <br>\n",
    "\n",
    "$\\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2$\n",
    "\n",
    "$\\qquad = (v_1^2 + v_2^2 + v_3^2)(w_1^2 + w_2^2 + w_3^2) - \\left( v_1^2w_1^2 + v_2^2w_2^2 + v_3^2w_3^2 + 2v_1w_1v_2w_2 + 2v_2w_2v_3w_3 + 2v_1w_1v_3w_3 \\right)$\n",
    "\n",
    "$\\qquad = v_1^2w_1^2 + v_1^2w_2^2 + v_1^2w_3^2 + v_2^2w_1^2 + v_2^2w_2^2 + v_2^2w_3^2 + v_3^2w_1^2 + v_3^2w_2^2 + v_3^2w_3^2 - \\left( v_1^2w_1^2 + v_2^2w_2^2 + v_3^2w_3^2 + 2v_1w_1v_2w_2 + 2v_2w_2v_3w_3 + 2v_1w_1v_3w_3 \\right)$\n",
    "\n",
    "$\\qquad = v_1^2w_1^2 + v_1^2w_2^2 + v_1^2w_3^2 + v_2^2w_1^2 + v_2^2w_2^2 + v_2^2w_3^2 + v_3^2w_1^2 + v_3^2w_2^2 + v_3^2w_3^2 - v_1^2w_1^2 - v_2^2w_2^2 - v_3^2w_3^2 - 2v_1w_1v_2w_2 - 2v_2w_2v_3w_3 - 2v_1w_1v_3w_3$\n",
    "\n",
    "\n",
    "$\\Rightarrow \\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2 = v_1^2w_2^2 + v_1^2w_3^2 + v_2^2w_1^2 + v_2^2w_3^2 + v_3^2w_1^2 + v_3^2w_2^2  - 2v_1w_1v_2w_2 - 2v_2w_2v_3w_3 - 2v_1w_1v_3w_3\\qquad\\qquad\\qquad.......eq(2)$\n",
    "\n",
    "As eq(1) and eq(2) are equal to each other, we can conclude: $\\lVert v \\times w \\rVert^2 = \\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2428d3f-ac94-4627-ba3f-71d5d707e4a1",
   "metadata": {},
   "source": [
    "<b>Solution 5.9 (b) </b>\n",
    "\n",
    "From part (a), we have established :\n",
    "\n",
    "$\\lVert v \\times w \\rVert^2 = \\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2$\n",
    "\n",
    "$\\Rightarrow \\lVert v \\times w \\rVert = \\sqrt{\\lVert v \\times w \\rVert^2}$\n",
    "\n",
    "$\\qquad\\qquad\\quad = \\sqrt{\\lVert v \\rVert^2 \\lVert w \\rVert^2 - (v \\cdot w)^2}\\qquad\\qquad\\quad \\qquad\\qquad\\quad ...eq(1)$\n",
    "\n",
    "We also know that, from dot product <br>\n",
    "\n",
    "$v \\cdot w = \\lVert v \\rVert \\lVert w \\rVert cos\\, \\theta$\n",
    "\n",
    "$\\Rightarrow (v \\cdot w)^2 = (\\lVert v \\rVert \\lVert w \\rVert cos\\, \\theta)^2$\n",
    "\n",
    "$\\qquad\\qquad\\quad  = (\\lVert v \\rVert)^2 (\\lVert w \\rVert)^2 cos^2\\, \\theta$\n",
    "\n",
    "Then, eq(1) can be written as:\n",
    "\n",
    "$\\lVert v \\times w \\rVert = \\sqrt{\\lVert v \\rVert^2 \\lVert w \\rVert^2 - \\lVert v \\rVert^2 \\lVert w \\rVert^2 cos^2\\, \\theta}$\n",
    "\n",
    "$\\qquad\\qquad = \\sqrt{\\lVert v \\rVert^2 \\lVert w \\rVert^2 (1- cos^2\\, \\theta)}$\n",
    "\n",
    "$\\qquad\\qquad = \\sqrt{\\lVert v \\rVert^2 \\lVert w \\rVert^2 sin^2\\theta}$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert v \\rVert \\lVert w \\rVert sin\\,\\theta$\n",
    "\n",
    "\n",
    "<b>Hence, proved, $\\lVert v \\times w \\rVert = \\lVert v \\rVert \\lVert w \\rVert sin\\,\\theta$</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4ce9379",
   "metadata": {},
   "source": [
    "<b>5.10</b> Do there exist non-zero vectors $v$ and $w$ in $\\mathbb{R}^3$ such that $v \\cdot w = 0$ and $v \\times w = 0$?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70df8316-e1a6-42c6-bb9d-51ccd5d74baf",
   "metadata": {},
   "source": [
    "<b>Solution 5.10</b>\n",
    "\n",
    "We know that, <br>\n",
    "\n",
    "$v \\cdot w = \\lVert v \\rVert \\lVert w \\rVert cos\\,\\theta$, \n",
    "\n",
    "and, $\\lVert v \\times w\\rVert =  \\lVert v \\rVert \\lVert w \\rVert sin\\,\\theta$\n",
    "\n",
    "Here, $v \\cdot w$ will be $0$ if $cos\\,t = 90^o$ or $270^o$, and $v \\times w$ will be $0$ if $sin\\,\\theta = 0^o$ or $180^0$\n",
    "\n",
    "Therefore, there do not exist non-zero vectors $v$ and $w$ such that $v \\cdot w = 0$ and $v \\times w = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65829c02",
   "metadata": {},
   "source": [
    "<b>5.11</b> In $\\mathbb{R}^3$, let $l$ be the line parametrized by $\\alpha(t) = a + tv$, and let $p$ be a point.\n",
    "\n",
    "\n",
    "<b>(a)</b> Show that the distance from $p$ to $l$ is given by the formula:\n",
    "\n",
    "$d = \\frac{\\lVert (p -a) \\times v \\rVert}{\\lVert v \\rVert}$\n",
    "\n",
    "<b>(b)</b> Find the distance from the point $p = (1, 1, -1)$ to the line parametrized by $\\alpha(t) = (2, 1, 2) + t(1, -2, 2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2fe2cc7",
   "metadata": {},
   "source": [
    "<b>5. 12 </b> True or False: $u \\times (v \\times w) = (u \\times w) \\times w$ for all $u, v, w$ in $\\mathbb{R}^3$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06a12ff3",
   "metadata": {},
   "source": [
    "<b>5. 13 </b> Let $u, v, w$ be points in $\\mathbb{R}^3$ such that $0, u, v, w$ are not coplanar. Prove that the volume of the parallelopiped determined by $u, v, w$ is equal to $| det[u \\, v \\, w] |$. (Hint: See figure 2.14 where $\\phi$ is the angle between $u$ and $v \\times w$. Keep in mind that $u$ and $v \\times w$ may lie on opposite sides of the plane spanned by $v$ and $w$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c2ef4ea",
   "metadata": {},
   "source": [
    "<b>5.14</b> Let $(u, v, w)$ be a basis of $\\mathbb{R}^3$, and let $\\theta$ be the angle between $v \\times w$ and $z$, where $0 \\le \\theta \\pi$, as usual. Use the definition of handedness to show that $\\theta \\lt$ if $(v, w, z)$ is right handed and $\\theta \\gt \\frac{\\pi}{2}$ if left-handed. Draw pictures to illustrate both situations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd726e56",
   "metadata": {},
   "source": [
    "<b>5.15</b> Strictly speaking, the cross product is defined only in $\\mathbb{R}^3$, but there is an analogous operation in $\\mathbb{R}^4$ if three factors area allowed. That is, given vectors $u, v, w$ in $\\mathbb{R}^4$ the product $u \\times v \\times w$ is a vector in $\\mathbb{R}^4$ that satisfies the property:\n",
    "\n",
    "$x \\cdot (u \\times v \\times w) = det[x \\, u \\, v \\, w]$\n",
    "\n",
    "for all $x$ in $\\mathbb{R}^4$, where the determinant is of the $4$ by $4$ matrix whose row are $x, u, v, w$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03fef442",
   "metadata": {},
   "source": [
    "<b>5.16</b> In general, the \"cross product\" in $\\mathbb{R}^n$ is a function of $n - 1$ factors. In $\\mathbb{R}^2$, this means that there is only one factor.\n",
    "\n",
    "<b>(a)</b> Given a vector $v = (a, b)$ in $\\mathbb{R}^2$, find a reasonable formula for \"vx\", and explain how you came up with it.\n",
    "\n",
    "<b>(b)</b> Draw a sketch that illustrates $v$ and your candidate for $vx$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a02b1bbd",
   "metadata": {},
   "source": [
    "------------------------------ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1c57aae",
   "metadata": {},
   "source": [
    "<h3>Section 6 The geometry of spaces curves: Frenet Vectors</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c86f8bcf",
   "metadata": {},
   "source": [
    "In Exercise 6.1 - 6.2, find the binormal $B(t)$ for the given path $\\alpha$. These problems are continuations of Exercise 4.1-4.2\n",
    "\n",
    "<b>6.1</b> $\\alpha(t) = (sin \\,4t, cos \\, 4t, 3t)$<br>\n",
    "<b>6.2</b> $\\alpha(t) =  (t, t^2 , 0)$<br>\n",
    "<b>6.3</b> Consider the line in $\\mathbb{R}^3$ parametrized by $\\alpha(t) = (1 + t, 1 + 2t, 1 + 3t)$. What happends when you try to find its frenet vectors $(T(t), N(t), B(t))$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3308a43b-a978-4186-a536-038a04005e1d",
   "metadata": {},
   "source": [
    "<b>Solution 6.1</b> \n",
    "\n",
    "We know that, <br>\n",
    "Binormal vector, $B(t) = T(t) \\times N(t)$, and we have from solution 4.1<br>\n",
    "\n",
    "$T(t) = (\\frac{4}{5}cos\\,4t, -\\frac{4}{5}sin\\,4t, \\frac{3}{5})$\n",
    "\n",
    "$N(t) = (-sin\\,4t, - cos\\,4t, 0)$\n",
    "\n",
    "$\\Rightarrow B(t) = T(t) \\times N(t) = det \\begin{bmatrix}\n",
    "i &j &k\\\\\n",
    "\\frac{4}{5}cos\\,4t& -\\frac{4}{5}sin\\,4t& \\frac{3}{5}\\\\\n",
    "-sin\\,4t& - cos\\,4t& 0\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\Rightarrow B(t) = (-\\frac{4}{5}sin\\,4t(0) - (-cos\\,4t)\\frac{3}{5})i - (\\frac{4}{5}cos\\,4t(0) -(-sin\\,4t)\\frac{3}{5}))j + (\\frac{4}{5}cos\\,4t(-cos\\,4t) - (-sin\\,4t)(-\\frac{4}{5}sin\\,4t))k$\n",
    "\n",
    "$\\Rightarrow B(t) = (\\frac{3}{5}cos\\,4t)i - (\\frac{3}{5}sin\\,4t)j + (-\\frac{4}{5}cos^2\\,4t - \\frac{4}{5}sin^2\\,4t)k$\n",
    "\n",
    "$\\Rightarrow B(t) = (\\frac{3}{5}cos\\,4t)i - (\\frac{3}{5}sin\\,4t)j + -\\frac{4}{5}(cos^2\\,4t + sin^2\\,4t)k$\n",
    "\n",
    "$\\Rightarrow B(t) = (\\frac{3}{5}cos\\,4t)i - (\\frac{3}{5}sin\\,4t)j + -\\frac{4}{5}k$\n",
    "\n",
    "$\\Rightarrow B(t) = (\\frac{3}{5}cos\\,4t, - \\frac{3}{5}sin\\,4t, -\\frac{4}{5})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32fa590a-8b22-461d-ade6-01c00b9530ab",
   "metadata": {},
   "source": [
    "<b>Solution 6.2</b>\n",
    "\n",
    "We know that, <br>\n",
    "Binormal vector $B(t) = T(t) \\times N(t)$, and we have from solution 4.2\n",
    "\n",
    "$T(t) = (\\frac{1}{\\sqrt{1 + 4t^2}}, \\frac{2t}{\\sqrt{1 + 4t^2}},0)$\n",
    "\n",
    "$N(t) = (- \\frac{2t}{(1+4t^2)^{1/2}}, \\frac{1}{(1+4t^2)^{1/2}}, 0)$\n",
    "\n",
    "$\\Rightarrow B(t) = T(t) \\times N(t) = det \\begin{bmatrix}\n",
    "i & j &k\\\\\n",
    "\\frac{1}{(1 + 4t^2)^{1/2}}& \\frac{2t}{(1 + 4t^2)^{1/2}}&0\\\\\n",
    "- \\frac{2t}{(1+4t^2)^{1/2}}& \\frac{1}{(1+4t^2)^{1/2}}& 0\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "Anything multiplied by $0$ yields $0$, therefore i, j would be $0$\n",
    "\n",
    "$\\Rightarrow B(t) = (0i, 0j , (\\frac{1}{(1+4t^2)^{1/2}} \\times \\frac{1}{(1+4t^2)^{1/2}} - (-\\frac{2t}{(1+4t^2)^{1/2}} \\times \\frac{2t}{(1+4t^2)^{1/2}})k)$\n",
    "\n",
    "$\\Rightarrow B(t) = \\left(0i, 0j , (\\frac{1}{1+4t^2} + \\frac{4t^2}{1+4t^2})k\\right)$\n",
    "\n",
    "$\\Rightarrow B(t) = \\left(0i, 0j , (\\frac{1+4t^2}{1+4t^2})k\\right)$\n",
    "\n",
    "$\\Rightarrow B(t) = (0, 0 , 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7aecc4d-04f6-436a-b68e-06c131158ea5",
   "metadata": {},
   "source": [
    "<b>Solution 6.3</b>\n",
    "\n",
    "We know that, <br>\n",
    "unit tangent vector, $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert} \\alpha'(t)$, principal normal, $N(t) =  \\frac{1}{\\lVert T'(t) \\rVert} T'(t)$ and Binormal vector $B(t) = T(t) \\times N(t)$\n",
    "\n",
    "and, we have $\\alpha(t) = (1 + t, 1 + 2t, 1 + 3t)$\n",
    "\n",
    "Here, $\\frac{d}{dt} (1 + t) = 0 + 1 = 1\\quad$, $\\frac{d}{dt} (1 + 2t) = 0 + 2 = 2\\quad$, and $\\frac{d}{dt} (1 + 3t) = 0 + 3 = 3$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t) = (1, 2, 3)$\n",
    "\n",
    "$\\Rightarrow \\lVert \\alpha'(t) \\rVert = \\lVert \\sqrt{1^2 + 2^2 + 3^2} \\rVert$<br>\n",
    "$\\qquad = \\lVert \\sqrt{1 + 4 + 9} \\rVert$<br>\n",
    "$\\qquad = \\lVert \\sqrt{14} \\rVert$\n",
    "\n",
    "$\\Rightarrow T(t) = \\frac{1}{\\sqrt{14}}(1,2,3)$\n",
    "\n",
    "Next, <br>\n",
    "$T'(t) = \\frac{d}{dt}(1,2,3)$<br>\n",
    "$\\qquad = (0,0,0)$\n",
    "\n",
    "Since, $T'(t) = (0,0,0)$ principal normal is undefined implying curve as straight line. <br>\n",
    "Similarly, Binormal Vector, $B(t)$ is undefined for $B(t) = T(t) \\times N(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d3dd92",
   "metadata": {},
   "source": [
    "---------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c0b5e3e",
   "metadata": {},
   "source": [
    "<h3>Section 7 Curvature and Torsion</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7975c539",
   "metadata": {},
   "source": [
    "<b>7.1</b> Find a parametrization of a curve that has constant curvature $\\frac{1}{2}$ and constant torsion $0$.\n",
    "\n",
    "<b>7.2</b> Find a parametrization of a curve that has constant curvature $\\frac{1}{2}$ and constant torsion $\\frac{1}{4}$\n",
    "\n",
    "<b>7.3</b> Prove the product rule for cross products. If $\\alpha$ and $\\beta$ are differentiable paths in $\\mathbb{R}^3$, then:\n",
    "\n",
    "$$(\\alpha \\times \\beta)' = \\alpha' \\times \\beta + \\alpha \\times \\beta'$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2be2a59-7c2d-4926-92ca-9ba671153503",
   "metadata": {},
   "source": [
    "<b>Solution 7.1</b> \n",
    "\n",
    "We know that, <br>\n",
    "Helix can be parametrized by: $\\alpha(t) = (a\\,cos\\,t, a\\,sin\\,t, bt)$, and curvature can be given by: $\\kappa = \\frac{a}{(a^2 + b^2)}$ and torsion $\\tau = \\frac{b}{a^2 + b^2}$\n",
    "\n",
    "We have, $\\kappa = \\frac{1}{2}$ and $\\tau = 0$.<br>\n",
    "In case of $\\tau = \\frac{b}{a^2 + b^2}$, we get, $0 = \\frac{b}{a^2 + b^2}$\n",
    "\n",
    "$\\Rightarrow b = 0$\n",
    "\n",
    "Then, in the case of $\\kappa = \\frac{a}{a^2 + b^2}$, we get:<br>\n",
    "$\\frac{1}{2} = \\frac{a}{a^2 + 0}$<br>\n",
    "$\\Rightarrow \\frac{1}{2} = \\frac{1}{a}$<br>\n",
    "$\\Rightarrow a = 2$\n",
    "\n",
    "Thus, parametrization of the curve : $\\alpha(t) = (2cos\\,t, 2\\,sin\\,t, 0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7263214-1204-46e8-8985-b09d81db96d5",
   "metadata": {},
   "source": [
    "<b>Solution 7.2</b><br>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ffb71fd",
   "metadata": {},
   "source": [
    "--------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bbeef7d",
   "metadata": {},
   "source": [
    "<h3>Section 9 : The Classification of Space Curves</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7873be26",
   "metadata": {},
   "source": [
    "9.1 Consider the curve parametrized by:<br>\n",
    "    $$ \\alpha(t) = (cos \\, t - sin \\,t, t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8fc0373",
   "metadata": {},
   "source": [
    "<b>(a)</b> Find the speed $v(t)$<br>\n",
    "<b>(b)</b> Find the unit target $T(t)$<br>\n",
    "<b>(c)</b> Find the principal normal $N(t)$<br>\n",
    "<b>(d)</b> Find the binormal $B(t)$<br>\n",
    "<b>(e)</b> Find the curvature $\\kappa(t)$<br>\n",
    "<b>(f)</b> Find the torsion $\\tau(t)$ <br>\n",
    "<b>(g)</b> The curve traced out by $\\alpha$ is congruent to a curve with a parametrization of the form $\\beta(t) = (a cos\\,t, a sin\\,t,bt)$ where $a$ and $b$ are constant and $a \\gt 0$. Find the values of $a$ and $b$. Then, sketch the curve traced out by $\\alpha$ and $\\beta$, and describe a motion of $\\mathbb(R)^3$ that takes the path $\\alpha$ and puts it right on top of $\\beta$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e0d0d58-aa8f-4b68-a8b3-6e00e95082bb",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b> \n",
    "\n",
    "We know that, speed $v(t) = \\lVert V(t) \\rVert$ or $\\lVert \\alpha'(t) \\rVert$\n",
    "\n",
    "Here, <br>\n",
    "$\\frac{d}{dt}cos\\,t = -sin\\,t \\quad$, $\\frac{d}{dt}-sin\\,t = -cos\\,t\\quad$, and $\\frac{d}{dt}t = 1$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t) = (-sin\\,t, -cos\\,t, 1)$<br>\n",
    "Therefore, speed, $v(t) = \\lVert \\sqrt{(-sin\\,t)^2 + (-cos\\,t)^2 + 1^2} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{sin^2t + cos^2t + 1} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\sqrt{2}$\n",
    "\n",
    "Thus, <b>speed $v(t) = \\sqrt{2}$</b>\n",
    "\n",
    "<b>Solution (b) </b><br>\n",
    "we know that, unit tengent $T(t)  = \\frac{1}{\\lVert \\alpha'(t) \\rVert}\\alpha'(t)$\n",
    "\n",
    "$\\Rightarrow T(t) = \\frac{1}{\\sqrt{2}}(-sin\\,t, -cos\\,t, 1)$\n",
    "\n",
    "<b>Solution (c)</b><br>\n",
    "We know that, principal normal, $N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t)$\n",
    "\n",
    "Here, $T(t) =\\left( -\\frac{1}{\\sqrt{2}}sin\\,t, -\\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{\\sqrt{2}}\\right)$\n",
    "\n",
    "and, $\\frac{d}{dt}(-\\frac{1}{\\sqrt{2}}sin\\,t) = - \\frac{1}{\\sqrt{2}}cos\\,t\\qquad$,\n",
    "$\\frac{d}{dt}(-\\frac{1}{\\sqrt{2}}cos\\,t) = \\frac{1}{\\sqrt{2}}sin\\,t\\qquad$\n",
    "$\\frac{d}{dt}(\\frac{1}{\\sqrt{2}}) = 0$\n",
    "\n",
    "$\\Rightarrow T'(t) = \\left( - \\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{\\sqrt{2}}sin\\,t, 0\\right)$\n",
    "\n",
    "$\\Rightarrow \\lVert T'(t) \\rVert = \\lVert \\sqrt{(- \\frac{1}{\\sqrt{2}}cos\\,t)^2 + (\\frac{1}{\\sqrt{2}}sin\\,t)^2 + 0^2} \\rVert$<br>\n",
    "$\\Rightarrow \\lVert T'(t) \\rVert = \\lVert \\sqrt{\\frac{1}{2}(cos^2\\,t + sin^2\\,t) + 0} \\rVert$<br>\n",
    "$\\Rightarrow \\lVert T'(t) \\rVert = \\frac{1}{\\sqrt{2}} $\n",
    "\n",
    "$\\Rightarrow N(t) = \\frac{1}{\\lVert T'(t) \\rVert} T'(t) = \\frac{1}{\\frac{1}{\\sqrt{2}}} \\left( - \\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{\\sqrt{2}}sin\\,t, 0\\right)$\n",
    "\n",
    "$\\qquad\\qquad = \\left( \\frac{\\sqrt{2}}{1}\\cdot -\\frac{1}{\\sqrt{2}}cos\\,t, \\frac{\\sqrt{2}}{1}\\cdot \\frac{1}{\\sqrt{2}}sin\\,t, \\frac{\\sqrt{2}}{1}\\cdot 0\\right)$\n",
    "\n",
    "$\\qquad\\qquad = (-cos\\,t, sin\\,t,0)$\n",
    "\n",
    "<b>Solution (d) </b> <br>\n",
    "\n",
    "We know that, <br>\n",
    "Binormal, $B(t) = T(t) \\times N(t)$\n",
    "\n",
    "$\\qquad B(t) = det \\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "-\\frac{sin\\,t}{\\sqrt{2}}&-\\frac{cos\\,t}{\\sqrt{2}}&\\frac{1}{\\sqrt{2}}\\\\\n",
    "-cos\\,t&sin\\,t&0\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\qquad = [(\\frac{-cos\\,t}{\\sqrt{2}}\\cdot0) - sin\\,t\\frac{1}{\\sqrt{2}})i - (\\frac{-sin\\,t}{\\sqrt{2}}\\cdot 0) - (-cos\\,t)\\frac{1}{\\sqrt{2}})j + (\\frac{-sin\\,t}{\\sqrt{2}}sin\\,t - (-cos\\,t)(\\frac{-cos\\,t}{\\sqrt{2}})k]$\n",
    "\n",
    "$\\qquad = -\\frac{sin\\,t}{\\sqrt{2}}i - \\frac{cos\\,t}{\\sqrt{2}}j + (\\frac{-sin^2\\,t}{\\sqrt{2}} -\\frac{cos^2\\,t}{\\sqrt{2}})k$\n",
    "\n",
    "$\\qquad = -\\frac{sin\\,t}{\\sqrt{2}}i - \\frac{cos\\,t}{\\sqrt{2}}j - \\frac{1}{\\sqrt{2}}(sin^2\\,t + cos^2\\,t)k$<br>\n",
    "$\\qquad = -\\frac{sin\\,t}{\\sqrt{2}}i - \\frac{cos\\,t}{\\sqrt{2}}j - \\frac{1}{\\sqrt{2}}k$<br>\n",
    "$\\qquad = \\left(-\\frac{sin\\,t}{\\sqrt{2}}, -\\frac{cos\\,t}{\\sqrt{2}},-\\frac{1}{\\sqrt{2}}\\right)$\n",
    "\n",
    "$\\Rightarrow B(t) = -\\frac{1}{\\sqrt{2}}(sin\\,t, cos\\,t, 1)$\n",
    "\n",
    "<b>Solution (e)</b><br>\n",
    "We know that, curvature $\\kappa(t) = \\frac{\\lVert T'(t) \\rVert}{v(t)}$\n",
    "\n",
    "$\\Rightarrow \\kappa(t) = \\frac{\\frac{1}{\\sqrt{2}}}{\\sqrt{2}} = \\frac{1}{2}$\n",
    "\n",
    "<b>Solution (f)</b><br>\n",
    "We know that, given $B'(t) = c(t)N(t)$, torsion is defined by $\\tau(t) = -\\frac{c(t)}{v(t)}$<br>\n",
    "We calculated $B(t) = -\\frac{1}{\\sqrt{2}}(sin\\,t, cos\\,t, 1)$\n",
    "\n",
    "Here, <br>\n",
    "$\\frac{d}{dt}\\left(-\\frac{1}{\\sqrt{2}}sin\\,t\\right) = -\\frac{1}{\\sqrt{2}}cos\\,t$<br>\n",
    "$\\frac{d}{dt}\\left(-\\frac{1}{\\sqrt{2}}cos\\,t\\right) = -\\frac{1}{\\sqrt{2}}(-sin\\,t) = \\frac{1}{2}sin\\,t$<br>\n",
    "$\\frac{d}{dt}1 =0$\n",
    "\n",
    "$\\Rightarrow B'(t) = (-\\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{2}sin\\,t, 0) = c(t)N(t)$<br>\n",
    "$\\Rightarrow (-\\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{2}sin\\,t, 0) = c(t)(-cos\\,t, sin\\,t, 0)$<br>\n",
    "$\\Rightarrow (-\\frac{1}{\\sqrt{2}}cos\\,t, \\frac{1}{2}sin\\,t, 0) = \\frac{1}{\\sqrt{2}}(-cos\\,t, sin\\,t, 0)$<br>\n",
    "\n",
    "$\\Rightarrow c(t) = \\frac{1}{\\sqrt{2}}$,<br>\n",
    "and, we have calculated $v(t) = \\frac{1}{\\sqrt{2}}$\n",
    "\n",
    "Therefore, torsion, $\\tau(t) = -\\frac{\\frac{1}{\\sqrt{2}}}{\\frac{1}{\\sqrt{2}}}$<br>\n",
    "\n",
    "$\\Rightarrow \\tau(t) = -\\frac{1}{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "132a673f",
   "metadata": {},
   "source": [
    "---------------- "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bcab6ee",
   "metadata": {},
   "source": [
    "<b>9.2</b> Let $\\alpha$ be the path defined by:\n",
    "\n",
    "$$ \\alpha(t) = (6 cos \\, t, 8 cos\\, t, 10 sin \\, t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3b25602",
   "metadata": {},
   "source": [
    "<b>(a)</b> Find the speed $v(t)$<br>\n",
    "<b>(b)</b> Find the unit tangent $T(t)$<br>\n",
    "<b>(c)</b> Find the principal normal $N(t)$<br>\n",
    "<b>(d)</b> Find the binormal $B(t)$<br>\n",
    "<b>(e)</b> Find the curvature $\\kappa(t)$<br>\n",
    "<b>(f)</b> Find the torsion $\\tau(t)$<br>\n",
    "<b>(g)</b> Based on your answers to parts $(e)$ and $(f)$, what can you say about the type of curve traced out by $\\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c9ae116-fadc-4804-af42-083897aa36e3",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b><br>\n",
    "We know that, speed $v(t) = \\lVert V(t) \\rVert = \\lVert \\alpha'(t) \\rVert$\n",
    "\n",
    "Here, $\\frac{d}{dt}6 cos\\,t = -6sin\\,t, \\frac{d}{dt}8 cos\\,t = -8sin\\,t$ and $\\frac{d}{dt}10sin\\,t = 10cos\\,t$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t) = (-6cos\\,t, -8sin\\,t, 10cos\\,t)$\n",
    "\n",
    "Therefore, speed $v(t) = \\lVert \\sqrt{(-6sin\\,t)^2 + (-8sin\\,t)^2 + (10cos\\,t)^2} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{36sin^2\\,t + 64sin^2\\,t + 100cos^2\\,t} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{100sin^2\\,t  + 100cos^2\\,t} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{100(sin^2\\,t  + cos^2\\,t)} \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{100} \\rVert$<br>\n",
    "\n",
    "$\\Rightarrow$ speed, $v(t) = 10$\n",
    "\n",
    "<b>Solution (b)</b><br>\n",
    "We know that, unit tangent vector $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert}\\alpha'(t)$\n",
    "\n",
    "$\\Rightarrow T(t) = \\frac{1}{10}(-6sin\\,t, -8sin\\,t, 10cos\\,t)$<br>\n",
    "$\\Rightarrow T(t) = -\\frac{3}{5}sin\\,t, -\\frac{4}{5}sin\\,t, cos\\,t$\n",
    "\n",
    "<b>Solution (c)</b><br>\n",
    "We know that, principal normal vector, $N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t)$\n",
    "\n",
    "Here, <br>\n",
    "$T(t) = -\\frac{3}{5}sin\\,t, -\\frac{4}{5}sin\\,t, cos\\,t$<br>\n",
    "\n",
    "and, $\\frac{d}{dt}(-\\frac{3}{5}sin\\,t) = -\\frac{3}{5}cos\\,t$<br>\n",
    "$\\qquad \\frac{d}{dt}(-\\frac{4}{5}sin\\,t) = -\\frac{4}{5}cos\\,t$<br>\n",
    "$\\qquad \\frac{d}{dt}cos\\,t = -sin\\,t$\n",
    "\n",
    "$\\Rightarrow T'(t) = (-\\frac{3}{5}cos\\,t, -\\frac{4}{5}cos\\,t, -sin\\,t)$\n",
    "\n",
    "Next, <br>\n",
    "$\\lVert T'(t) \\rVert  = \\lVert \\sqrt{(-\\frac{3}{5}cos\\,t)^2 + (-\\frac{4}{5}cos\\,t)^2 + (-sin\\,t)^2} \\rVert$\n",
    "\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{9}{25}cos^2\\,t + \\frac{16}{25}cos^2\\,t + sin^2\\,t } \\rVert $<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{25}{25}cos^2\\,t  + sin^2\\,t } \\rVert $<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{cos^2\\,t  + sin^2\\,t } \\rVert $\n",
    "\n",
    "$\\Rightarrow \\lVert T'(t) \\rVert  = 1$\n",
    "\n",
    "Therefore, principal normal vector, $N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t) = \\frac{1}{1}(-\\frac{3}{5}cos\\,t, -\\frac{4}{5}cos\\,t, -sin\\,t)$\n",
    "\n",
    "$\\Rightarrow N(t) = (-\\frac{3}{5}cos\\,t, -\\frac{4}{5}cos\\,t, -sin\\,t)$\n",
    "\n",
    "<b>Solution (d) </b> <br>\n",
    "\n",
    "We know that, <br>\n",
    "Binormal, $B(t) = T(t) \\times N(t)$\n",
    "\n",
    "$\\qquad B(t) = det\\begin{bmatrix}\n",
    "i&j&k\\\\\n",
    "-\\frac{3}{5}sin\\,t&-\\frac{4}{5}sin\\,t&cos\\,t\\\\\n",
    "-\\frac{3}{5}cos\\,t&-\\frac{4}{5}cos\\,t&-sin\\,t\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$\\qquad = [((-\\frac{4}{5}sin\\,t)(-sin\\,t) - (-\\frac{4}{5}cos\\,t)cos\\,t)i - ((-\\frac{3}{5}sin\\,t)(-sin\\,t) - (-\\frac{3}{5}cos\\,t)cos\\,t)j +\n",
    "((-\\frac{3}{5}sin\\,t)(-\\frac{4}{5}cos\\,t)- (-\\frac{3}{5}cos\\,t)(-\\frac{4}{5}sin\\,t))k]$<br>\n",
    "\n",
    "$\\qquad = (\\frac{4}{5}sin^2t + \\frac{4}{5}cos^2t)i - (\\frac{3}{5}sin^2t + \\frac{3}{5}cos^2t)j + (\\frac{12}{25}sin\\,tcos\\,t - \\frac{12}{25}sin\\,tcos\\,t)k$<br>\n",
    "\n",
    "$\\qquad = \\frac{4}{5}(sin^2t + cos^2t)i - \\frac{3}{5}(sin^2t + cos^2t)j + 0k$<br>\n",
    "$\\qquad = \\frac{4}{5}i - \\frac{3}{5}j + 0k$\n",
    "\n",
    "$\\Rightarrow B(t) = \\left(\\frac{4}{5}, -\\frac{3}{5}, 0\\right)$\n",
    "\n",
    "<b>Solution (e)</b><br>\n",
    "We know that, curvature $\\kappa(t) = \\frac{\\lVert T'(t) \\rVert}{v(t)}$\n",
    "\n",
    "$\\qquad\\qquad \\Rightarrow \\kappa(t) = \\frac{1}{10}$\n",
    "\n",
    "<b>Solution (f)</b><br>\n",
    "We know that, given $B'(t) = c(t)N(t)$, torsion is defined by $\\tau(t) = -\\frac{c(t)}{v(t)}$<br>\n",
    "We calculated $B(t) = \\left(\\frac{4}{5}, -\\frac{3}{5}, 0\\right)$\n",
    "\n",
    "$\\Rightarrow B'(t) = (0,0,0)$\n",
    "\n",
    "$\\Rightarrow (0,0,0) = c(t)(-\\frac{3}{5}cos\\,t, -\\frac{4}{5}cos\\,t, -sin\\,t)$\n",
    "\n",
    "$\\Rightarrow c(t) = 0$\n",
    "\n",
    "Therefore, torsion, $\\tau(t) = -\\frac{c(t)}{v(t)} = \\frac{0}{10}$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad \\tau(t)= 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "548357fc-e88c-4d51-a3cb-5ac2f7c99fa3",
   "metadata": {},
   "source": [
    "<b>Solution (g)</b><br>\n",
    "\n",
    "Here, curvature $\\kappa(t) = \\frac{1}{10}$. As curvature is non-zero, it means it is not a straight line, and as curvature is constant, it means curve traces out a circular path with constant radius. <br>\n",
    "Also, torsion, $\\tau(t) = 0$ means curve is not wobbling, and lies entirely in a plane "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6648d11",
   "metadata": {},
   "source": [
    "---------------------------- "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ba0c010",
   "metadata": {},
   "source": [
    "<b>9.3</b> Let $\\alpha$ be the path defined by:\n",
    "\n",
    "$$\\alpha(t) = (t + \\sqrt{3} sin \\,t, \\sqrt{3} t - sin\\,t, 2\\,cos\\,t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb10b04b",
   "metadata": {},
   "source": [
    "The following calculations are kind of messy, but the conclusion may be unexpected.\n",
    "\n",
    "<b>(a)</b> Find the speed $v(t)$<br>\n",
    "<b>(b)</b> Find the unit tangent $T(t)$<br>\n",
    "<b>(c)</b> Find the principal normal $N(t)$<br>\n",
    "<b>(d)</b> Find the binormal $B(t)$<br>\n",
    "<b>(e)</b> Find the curvature $\\kappa(t)$<br>\n",
    "<b>(f)</b> Find the torsion $\\tau(t)$<br>\n",
    "<b>(g)</b> Based on your answers to parts $(e)$ and $(f)$, what can you say about the type of curve traced out by $\\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ff30dd-b0ae-4597-89be-e090776edca8",
   "metadata": {},
   "source": [
    "<b>Solution (a)</b><br>\n",
    "We know that, speed $v(t) = \\lVert V(t) \\rVert = \\lVert \\alpha'(t) \\rVert$<br>\n",
    "Here, <br>\n",
    "$\\frac{d}{dt}(t + \\sqrt{3}sin\\,t) = 1 + \\sqrt{3}cos\\,t$<br>\n",
    "$\\frac{d}{dt}\\sqrt{3}t - sin\\,t = \\sqrt{3} - cos\\,t$, and $\\frac{d}{dt}2cos\\,t = -2sin\\,t$\n",
    "\n",
    "$\\Rightarrow \\alpha'(t) = (1 + \\sqrt{3}cos\\,t, \\sqrt{3} - cos\\,t, -2sin\\,t )$\n",
    "\n",
    "Therefore, speed, $v(t) = \\lVert \\alpha'(t) \\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{(1 + \\sqrt{3}cos\\,t)^2, (\\sqrt{3} - cos\\,t)^2 + (-2sin\\,t)^2 }\\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{(1 + 3cos^2t +2\\sqrt{3}cos\\,t +3+ cos^2t - 2\\sqrt{3}cos\\,t + 4sin^2t }\\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{(4 + 4cos^2t + 4sin^2t }\\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{(4 + 4(cos^2t + sin^2t) }\\rVert$<br>\n",
    "$\\qquad\\qquad\\qquad\\qquad\\quad = \\lVert \\sqrt{(4 + 4)}\\rVert$<br>\n",
    "Hence, speed, $v(t) = \\sqrt{8}$\n",
    "\n",
    "<b>Solution (b)</b><br>\n",
    "We know that, unit tangent vector $T(t) = \\frac{1}{\\lVert \\alpha'(t) \\rVert}\\alpha'(t)$\n",
    "\n",
    "$\\Rightarrow T(t) = \\frac{1}{\\sqrt{8}}(1 + \\sqrt{3}cos\\,t, \\sqrt{3} - cos\\,t, -2sin\\,t)$\n",
    "\n",
    "<b>Solution(c)</b><br>\n",
    "\n",
    "Here,\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{1}{\\sqrt{8}}+\\frac{\\sqrt{3}}{\\sqrt{8}}cos\\,t) = 0 -\\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t = -\\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t$<br>\n",
    "$\\frac{d}{dt}(\\frac{\\sqrt{3}}{\\sqrt{8}} - \\frac{1}{\\sqrt{8}}cos\\,t) = 0 -(\\frac{1}{\\sqrt{8}}sin\\,t) = \\frac{1}{\\sqrt{8}}sin\\,t$<br>\n",
    "$\\frac{d}{dt}\\frac{-2}{\\sqrt{8}}sin\\,t = \\frac{-2}{\\sqrt{8}}cos\\,t = -\\frac{1}{\\sqrt{2}}cos\\,t$\n",
    "\n",
    "$\\Rightarrow T'(t) = \\left(-\\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t, \\frac{1}{\\sqrt{8}}sin\\,t, -\\frac{1}{\\sqrt{2}}cos\\,t\\right)$\n",
    "\n",
    "$\\lVert T'(t) \\rVert = \\lVert \\sqrt{ (-\\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t)^2 + (\\frac{1}{\\sqrt{8}}sin\\,t)^2 + (-\\frac{1}{\\sqrt{2}}cos\\,t)^2 } \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{3}{8}sin^2\\,t + \\frac{1}{8}sin^2\\,t + \\frac{1}{2}cos^2\\,t} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{1}{2}sin^2\\,t + \\frac{1}{2}cos^2\\,t} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{1}{2}(sin^2\\,t + cos^2\\,t)} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\lVert \\sqrt{\\frac{1}{2}} \\rVert$<br>\n",
    "$\\qquad\\qquad = \\frac{1}{\\sqrt{2}}$\n",
    "\n",
    "Then, we know that<br>\n",
    "$N(t) = \\frac{1}{\\lVert T'(t) \\rVert}T'(t) = \\frac{1}{1/\\sqrt{2}}\\left(-\\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t, \\frac{1}{\\sqrt{8}}sin\\,t, -\\frac{1}{\\sqrt{2}}cos\\,t\\right)$\n",
    "\n",
    "$\\Rightarrow N(t) = \\sqrt{2}\\left(\\frac{-\\sqrt{3}}{2\\sqrt{2}}sin\\,t, \\frac{1}{2\\sqrt{2}}sin\\,t, -\\frac{1}{\\sqrt{2}}cos\\,t\\right)$\n",
    "\n",
    "$\\Rightarrow N(t) = \\left(\\frac{-\\sqrt{3}}{2}sin\\,t, \\frac{1}{2}sin\\,t, -cos\\,t\\right)$\n",
    "\n",
    "$\\Rightarrow N(t) = \\frac{1}{2}\\left(-\\sqrt{3}sin\\,t, sin\\,t, -2cos\\,t\\right)$\n",
    "\n",
    "\n",
    "<b>Solution (d)</b>\n",
    "\n",
    "We know that, <br>\n",
    "Binormal, $B(t) = T(t) \\times N(t)$\n",
    "\n",
    "$\\Rightarrow B(t) = det\\begin{bmatrix}\n",
    "i & j & k\\\\\n",
    "\\frac{1-\\sqrt{3}cos\\,t}{\\sqrt{8}}&\\frac{\\sqrt{3} - cos\\,t}{\\sqrt{8}}&\\frac{-2}{\\sqrt{8}}sin\\,t\\\\\n",
    "-\\frac{\\sqrt{3}}{2}sin\\,t&\\frac{1}{2}sin\\,t&-cos\\,t\\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "$= \\left(\\frac{\\sqrt{3}-cos\\,t}{\\sqrt{8}}(-cos\\,t) - \\frac{1}{2}sin\\,t(-\\frac{2}{\\sqrt{8}}sin\\,t)\\right)i - \\left(\\frac{1+\\sqrt{3}}{\\sqrt{8}}(-cos\\,t) + \\frac{\\sqrt{3}}{2}sin\\,t(-\\frac{2}{\\sqrt{8}}sin\\,t)\\right)j + \\left(\\frac{1+\\sqrt{3}cos\\,t}{\\sqrt{8}}\\cdot\\frac{1}{2}sin\\,t + (\\frac{\\sqrt{3}}{2}sin\\,t\\cdot\\frac{\\sqrt{3} - cos\\,t}{\\sqrt{8}})\\right)k$\n",
    "\n",
    "$=\\left(\\frac{-\\sqrt{3}cos\\,t + cos^2\\,t}{\\sqrt{8}} + \\frac{sin^2\\,t}{\\sqrt{8}}\\right)i - \\left(\\frac{-cos\\,t -\\sqrt{3}cos^2\\,t}{\\sqrt{8}} - \\frac{\\sqrt{3}sin^2\\,t}{\\sqrt{8}}\\right)j + \\left(\\frac{sin\\,t + \\sqrt{3}cos\\,t\\,sin\\,t}{2\\sqrt{8}} + \\frac{3sin\\,t - \\sqrt{3}cos\\,tsin\\,t}{2\\sqrt{8}}\\right)k$\n",
    "\n",
    "$ = \\left(\\frac{1 - \\sqrt{3}cos\\,t}{\\sqrt{8}}\\right)i +\\left(\\frac{\\sqrt{3}(cos^2\\,t +sin^2\\,t) + cos\\,t}{\\sqrt{8}}\\right)j + \\left(\\frac{4sin\\,t}{2\\sqrt{8}}\\right)k$\n",
    "\n",
    "$ = \\left(\\frac{1 - \\sqrt{3}cos\\,t}{\\sqrt{8}}\\right)i +\\left(\\frac{\\sqrt{3} +cos\\,t}{\\sqrt{8}}\\right)j + \\left(\\frac{4sin\\,t}{2\\sqrt{8}}\\right)k$\n",
    "\n",
    "$ = \\left(\\frac{1 - \\sqrt{3}cos\\,t}{\\sqrt{8}} ,\\frac{\\sqrt{3} +cos\\,t}{\\sqrt{8}}, \\frac{4sin\\,t}{2\\sqrt{8}}\\right)$\n",
    "\n",
    "$\\Rightarrow B(t) = \\frac{1}{\\sqrt{8}} \\left(1 - \\sqrt{3}cos\\,t ,\\sqrt{3} +cos\\,t, 2sin\\,t\\right)$\n",
    "\n",
    "<b>Solution (e)</b><br>\n",
    "\n",
    "We know that, curvature $\\kappa(t) = \\frac{\\lVert T'(t) \\rVert}{v(t)}$\n",
    "\n",
    "$\\Rightarrow \\kappa(t) = \\frac{\\frac{1}{\\sqrt{2}}}{\\sqrt{8}} = \\frac{1}{\\sqrt{16}}$\n",
    "\n",
    "Therefore, curvature, $\\kappa(t) = \\frac{1}{4}$\n",
    "\n",
    "\n",
    "<b>Solution (f)</b><br>\n",
    "We know that, given $B'(t) = c(t)N(t)$, torsion is defined by $\\tau(t) = -\\frac{c(t)}{v(t)}$<br>\n",
    "\n",
    "Here, $B(t) =  \\left(\\frac{1 - \\sqrt{3}cos\\,t}{\\sqrt{8}} ,\\frac{\\sqrt{3} +cos\\,t}{\\sqrt{8}}, \\frac{4sin\\,t}{2\\sqrt{8}}\\right)$\n",
    "\n",
    "Next, <br>\n",
    "$\\frac{d}{dt}(\\frac{1}{\\sqrt{8}} - \\frac{\\sqrt{3}}{\\sqrt{8}}cos\\,t) = \\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t$<br>\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{\\sqrt{3}}{\\sqrt{8}} + \\frac{cos\\,t}{\\sqrt{8}}) = -\\frac{1}{\\sqrt{8}}sin\\,t$<br>\n",
    "\n",
    "$\\frac{d}{dt}(\\frac{2}{\\sqrt{8}}sin\\,t) = \\frac{2}{\\sqrt{8}}cos\\,t$\n",
    "\n",
    "$\\Rightarrow B'(t) = \\frac{\\sqrt{3}}{\\sqrt{8}}sin\\,t, -\\frac{1}{\\sqrt{8}}sin\\,t, \\frac{2}{\\sqrt{8}}cos\\,t$\n",
    "\n",
    "or $B'(t) = -\\frac{1}{\\sqrt{8}}(-\\sqrt{3}sin\\,t, sin\\,t -2cos\\,t)$\n",
    "\n",
    "We have, $N(t) = \\frac{1}{2}\\left(-\\sqrt{3}sin\\,t, sin\\,t, -2cos\\,t\\right)$\n",
    "\n",
    "$\\Rightarrow  -\\frac{1}{\\sqrt{8}}(-\\sqrt{3}sin\\,t, sin\\,t -2cos\\,t) = c(t)\\frac{1}{2}\\left(-\\sqrt{3}sin\\,t, sin\\,t, -2cos\\,t\\right)$\n",
    "\n",
    "$\\Rightarrow c(t) = \\frac{-\\frac{1}{\\sqrt{8}}}{\\frac{1}{2}}$<br>\n",
    "\n",
    "$\\Rightarrow c(t) = - \\frac{1}{\\sqrt{2}}$\n",
    "\n",
    "$\\Rightarrow$ torsion, $\\tau(t) = -\\frac{c(t)}{v(t)} = -\\frac{-\\frac{1}{\\sqrt{2}}}{\\sqrt{8}}$\n",
    "\n",
    "Hence, the torsion $\\tau(t) = \\frac{1}{4}$\n",
    "\n",
    "<b>Solution (g) </b><br>\n",
    "\n",
    "Since, we calculated both the curvature, $\\kappa(t)$ and torsion, $\\tau(t)$ as constant $\\frac{1}{4}$. This implying path traced out by parametrization is circular helix."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bb0aa82",
   "metadata": {},
   "source": [
    "------------------ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bba0c96f",
   "metadata": {},
   "source": [
    "In Exercises 9.4 - 9.8, $\\alpha$ is a path in $\\mathbb{R}^3$ with velocity $V(t)$, speed $v(t)$, acceleration $a(t)$ and Frenet Vectors $T(t), N(t)$ and $B(t)$. You may assume that $v(t) \\ne 0$ and $T'(t) \\ne 0$ for all $t$ so that the Frenet vectors are defined:<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e87d787",
   "metadata": {},
   "source": [
    "<b>9.4 </b> Prove the following statements:\n",
    "\n",
    "<b>(a)</b> $V = v(t)$<br>\n",
    "\n",
    "<b>(b)</b> $a =v'(T) + \\kappa v^2 N$ (Hence, $v'$ is the tangential component of acceleration and $\\kappa v^2$, the normal component)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aa046e0",
   "metadata": {},
   "source": [
    "<b>9.5</b> Prove that $v \\cdot a = vv'$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73ab1722",
   "metadata": {},
   "source": [
    "<b> 9.6</b> Show that the curvature is given by $\\frac{\\lvert v \\times a \\rvert}{v^3}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fa5c640",
   "metadata": {},
   "source": [
    "<b> 9.7 </b> Let $C$ be the curve in $\\mathbb{R}^3$ parametrized by $\\alpha(t) = (t, t^2, t^3)$. Use the formula from the previous exercise to find the curvature at the point $(1,1,1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d709daa",
   "metadata": {},
   "source": [
    "<b>9.8</b> According to 9.4, the velocity and acceleration vectors lie in the plane spanned by $T$ and $N$. Thus like the binormal vector $B$, the cross product $v \\times a$ is orthogonal to that plane. It follows that the unit vector in the direction of $v \\times a$ must be $\\pm B$. Show that in fact it is $B$. In other words, show that $B = \\frac{v \\times a}{\\lvert v \\times a \\rvert}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a694ed4f",
   "metadata": {},
   "source": [
    "<b>9.9</b> Let $\\alpha(t) = (2 cos\\,t, 2 sin\\,t, 2 cos\\,t)$<br>\n",
    "\n",
    "<b>(a)</b> Find the curvature $\\kappa(t)$. (You may use the result of Exercise 9.6 if you wish)\n",
    "\n",
    "<b>(b)</b> For the curve, what does $v \\times a$ tell you about the torsion $\\tau(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efa6edc0",
   "metadata": {},
   "source": [
    "<b>9.10 </b> Let $\\alpha$ be a path in $\\mathbb{R}^3$ such that $v \\ne 0$ and $T' \\ne 0$ and let:\n",
    "\n",
    "$$ w = \\tau v T + \\kappa v B $$\n",
    "\n",
    "Prove the <b>Darboux Formulas:</b>\n",
    "\n",
    "$w \\times T = T'$<br>\n",
    "$w \\times N = N'$<br>\n",
    "$w \\times B = B'$<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30dcb3cc",
   "metadata": {},
   "source": [
    "<b>9.11</b>\n",
    "\n",
    "Suppose that the Darboux vector $w = \\tau v T + \\kappa v B$ from the previous exercise is a constant vector.\n",
    "\n",
    "<b>(a)</b>Prove that $\\tau v$ and $\\kappa v$ are both constant. (Hint: Calculate $w'$ and use the Frenet-Serret formulas. Note that $T$ and $B$ need not be constant even if $w$ is)\n",
    "\n",
    "<b>(b)</b>If $\\alpha$ has constant speed, prove that $\\alpha$ is congruent to a helix."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0007310",
   "metadata": {},
   "source": [
    "<b>9.12</b> let $\\alpha$ be a path in $\\mathbb{R}^3$ that lies on  the sphere of radius $a$ centered at the origin, that is:\n",
    "\n",
    "$\\lVert \\alpha(t) \\rVert = a\\quad$ for all $t$\n",
    "\n",
    "Let $T(t)$ be the unit tangent, $N(t)$ the principal normal, $v(t)$ the speed, and $\\kappa(t)$ the curvature. Assume that $v(t) \\ne 0$ and $T'(t) \\ne 0$ for all $t$ so that the Frenet vectors are defined.\n",
    "\n",
    "<b>(a)</b> Show that $\\alpha(t) \\cdot T(t) = 0$ for all $t$<br>\n",
    "<b>(b)</b> Show that $\\kappa(t)\\alpha(t) \\cdot N(t) = -1$ for all $t$. (Hint: Differentiate part (a)).<br>\n",
    "<b>(c)</b> Show that $\\kappa(t) \\ge \\frac{1}{a}$ for all $t$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d051dcb",
   "metadata": {},
   "source": [
    "<b>9.13</b><br>\n",
    "Let $\\alpha$ be a path in $\\mathbb{R}^3$ that has:<br>\n",
    "- constant speed $v = 1$\n",
    "- positive torsion $\\tau (t)$, and \n",
    "- binormal vector $B(t) = (-\\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{2}}{2} sin \\, 2t, \\frac{\\sqrt{2}}{2} cos\\,2t)$\n",
    "\n",
    "<b>(a)</b> Find, in whatever order you wish, the unit tangent $T(t)$, the principal normal $N(t)$ the curvature $\\kappa(t)$, and the torsion $\\tau (t)$\n",
    "\n",
    "<b>(b)</b> In addition, if $\\alpha(0) = (0,0,0)$, find a formula for $\\alpha(t)$ as a function of $t$ (Hint: Use your formula for $T(t)$)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f4a6383",
   "metadata": {},
   "source": [
    "<b>9.14</b> In this problem, we determine the effect of a reflection, specifically, the reflection in the $xy-$plane, on the Frenet Vectors, the speed, the curvature, and the torsion of a path. To fix some notation, if $p = (x,y,z)$  is a point of $\\mathbb{R}^3$ let $p^* = (x, y, -z)$ denote its reflection in the $xy$-plane.\n",
    "\n",
    "Now, let $\\alpha(t) = (x(t), y(t), z(t))$ be a path in $\\mathbb{R}^3$ whose Frenet vectors are defined for all $t$, and let $\\beta(t)$ be its reflection:<br>\n",
    "$ \\beta(t) = \\alpha(t)^* = (x(t), y(t), -z(t))$\n",
    "\n",
    "<b>(a)</b> Show that $\\alpha$ and $\\beta$ have the same speed $v$.<br>\n",
    "<b>(b)</b> Show the unit tangent vectors of $\\alpha$ and $\\beta$ are related by $T_{\\beta} = T_{\\alpha}^*$ i.e, they are also reflections of one another.<br>\n",
    "\n",
    "<b>(c)</b> Similarly, show that the principal normals are reflections: $N_{\\beta} = N_{\\beta}^*$\n",
    "\n",
    "<b>(d)</b> Show that $\\alpha$ and $\\beta$ have the same curvature: $\\kappa_{\\alpha} = \\kappa_{\\beta}$\n",
    "\n",
    "<b>(e)</b>Show that the binormals are related in the following way: if $B_{\\alpha} = (b_1, b_2, b_3)$ then $B_{\\beta} = (-b_1, -b_2, b_3) = -B_{\\alpha}^*$\n",
    "\n",
    "<b>(f)</b>Describe how the torsions $\\tau_{\\alpha}$ and $\\tau_{\\beta}$ of the paths are related (Hint: Use part (c) and (e).)"
   ]
  }
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