1_4 Analytic Geometry, 해석 기하.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:238: RuntimeWarning: Glyph 54217 missing from current font.\n",
      "  font.set_text(s, 0.0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:238: RuntimeWarning: Glyph 54665 missing from current font.\n",
      "  font.set_text(s, 0.0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:238: RuntimeWarning: Glyph 51060 missing from current font.\n",
      "  font.set_text(s, 0.0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:238: RuntimeWarning: Glyph 46041 missing from current font.\n",
      "  font.set_text(s, 0.0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:201: RuntimeWarning: Glyph 54217 missing from current font.\n",
      "  font.set_text(s, 0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:201: RuntimeWarning: Glyph 54665 missing from current font.\n",
      "  font.set_text(s, 0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:201: RuntimeWarning: Glyph 51060 missing from current font.\n",
      "  font.set_text(s, 0, flags=flags)\n",
      "C:\\Users\\LG\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:201: RuntimeWarning: Glyph 46041 missing from current font.\n",
      "  font.set_text(s, 0, flags=flags)\n"
     ]
    },
    {
     "data": {
      "image/png": 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AmYo2nrFq/fr1+te/jGe1zj33XF100UUKh8M0nkFSefXVVxQKRZcude9+sez2I/9vdOTIh9SqVSs1aNDokFnvt96aW2rjPFoWi1VnnHGWbr75NjVv3rLQurp16+nBB8epWrXqmjPnJUnS/v37NGvWv3XvvQ8c9hw2m03du1+smTOfVzgc1quvvqy+fQeZ+nUAyYjlIgDKjMUi+XzRLfsGDhxouCOD1WqNN57JyQkk7dvsqHjy8/P03ntvxz+/4IKLjup1559/gRo2bHzEZSWJ0LJlK02YMPWwAftgd975z0NmuRct+uioXnfw9+q9995Vbm5u0QYKpCBCNoAy4/W6ZLVa9emnn2revHmGNb1791b79u0VCoWVm8ssNpLHp58uUnZ2tiSpSZOmR3XjX3njcDh08smnxj/fsWO78vLyjvi6Bg0aqlmzFpKk3Nwcffrpx6U2RiBZELIBlIlo45noNmeFNZ7xer3xGyG52RHJ5pNPFsY/7tz5tASOJLEyMjIO+fxo978++Hv28ccLD1MJlA+EbABlwudzyWKxaPbs2fr6668Na/r166e6devSeAZJJxAIaMWKZfHPTzihUwJHk1jbtm2Nf2y1WpWRUfmoXtehQ8f4x998s1z5+fwhjfKNkA2g1MUaz+Tm5mro0KGGNbVr19bAgQMlMYuN5PPjj6sP2eauTZu2CRxN4uTn52np0i/jn7dq1eaobv6UpNat28U/zsvL0+rV35s+PiCZELIBlLq0NLck6ZFHHtGvv/5qWDN27FilpaUpPz9A4xkknbVr18Q/rl69xlHP3pY3r732X2Vl/bU8pFu37kf92rS0NNWpUzf++cHfU6A8ImQDKFVOp10Oh007d+7UxIkTDWuOPfZY3XzzzTSeQdLavHlz/OOKusfzTz9t1AsvPBv/vF69+rrkksuLdIx69eofdLxNpo0NSEaEbAClKtZ4ZtSoUTpw4IBhzZQpU2S1WpWbG1AoxJZ9SD7btv0e/7h69RoJHEli7NuXqaFDB8jvj/4RbLPZNHTog3I4HEU6zsHb/23fvs3UMQLJhpANoNR4PNHGM2vWrNGzzz5rWNOtWzd169ZN4XBYOTls2YfklJmZGf+4UqVKiRtIAuTn52nw4H767be/lnrddttdat/++CIfKz09Pf7x3r17zBgekLQI2QBKhcUieb3RxjMDBgyId8k7mM1m09SpUyVJOTl+Gs8gaeXl/dU8xeVyJ3AkZSsQCGjo0IH6/vtV8ceuvPIa9ep1Y7GOd/D3joY0KO8I2QBKRazxzEcffaT58+cb1tx0001q167dn41nCnZ/BJJRRfljMBgMasSIQYfsJnLxxZfr//5vQLGPWVG+d4BEyAZQCmKNZ8LhcKGNZ9LS0jR27FhJbNmH5Od2e+IfV4T9nYPBoB58cKi++OKz+GMXXXSJBg4cWqL28LE13ZLk8XgOUwmkPkI2ANOlpUUbz8ycOVOrVq0yrBk4cKBq165N4xmkhMqVK8c/3r9/X+IGUgZCoZDGjBmhRYv+an3evfvFGjRoeIkCtiTt378//nGVKlVLdCwg2RGyAZjKbrfJ5XIoJydHw4cPN6ypV69efIY7KyuvLIcHFEudOvXiH+/atTOBIyldoVBIY8eO1Mcffxh/7MIL/6HBg0fIai15ZNi586/vXe3adUp8PCCZEbIBmCotLbpl39SpU7V161bDmoceekher1f5+QEFg+GyHB5QLE2aNI1//Pvvxg2VUl0oFNJDD43SwoUL4o9dcMFFGjJkpCkBWzr0e9e0aTNTjgkkK0I2ANO4XNHGM9u2bdPkyZMNa44//nj17t1bkUhEWVnlf20ryofWrdvEP969e7f27t2bwNGYLxwOa/z4B/Xhh+/HH+vWrbuGDh1lWsDOyso6ZG/sg7+nQHlEyAZgmljjmREjRig7O9uwZtq0afHGM+EwOw0gNbRq1UYejzf++Zo1PyRwNFH//OftOv30TvH/iiscDmvChDFasOC9+GPdul2oYcMeNC1gS4d+z9xut9q0aWfasYFkRMgGYAqPxyGbzarvv/9e//73vw1rLrroIp1zzjl/Np5hFhupw+FwqFOnE+Off/PNigSOxjyRSERTpozXe++9E3/s/PMv1LBho00N2NKh37MOHTrJ5XKZenwg2dgTPQAApSsSiWjlyq/18ccLtW7dGm3btk3Z2VmSJJ/Pp1q16qhp02PUrt1xOu20M4rVMtpiscQbz/Tv31/hcMF11na7XVOmTJEUazxTgi8KSICzz+6qzz//VJL01Vdf6N57Hziq1/3nP8/pxRdfKPB4IPDX3vCrVq3UOeecWqCmW7fuGjTI+AZiM3z88UK9/fb/4p9bLBbt2bNb/fvff9THuPvu+9SsWfMj1i1Z8td+22ef3bVI4wRSESEbKMfWrv1RkyeP0/r1aw2fz8zMVGZmptat+1HvvfeOXnihmubNW2BYezg+n1NWq1Xvv/++PvjgA8Oa2267Ta1bt1YwGKLxDFLSmWeeLa/Xp5ycbP3yy8/66adNatr0mCO+LhQKye/3H7YmEokY1gSDhW9veXBb8mbNWhxxHEby8w/d3ScSiWjFimVFOkavXn2OWPPbb79q48b1kqL7Y3fpck6RzgGkIpaLAOXUsmVLdM89tx4SsNPS0tW6dRt16nSSjjvueNWv3+CQt4RbtGhV5PPYbBa53Q6FQiENGGDcCa5SpUoaPXq0JCk7+/BhA0hWbrdb3bv/I/75ggXGnUzLwt69e/Tzz1vin990060JG8vROPh71a1bd3m93sNUA+UDM9lAObR37x49+OCweGe6jh1P1C233KFjj21foJlETk6Oli9fovnz3y5WyPb5oo1nXnjhBf3wg/HNYIMHD1aNGjUUCATl99N4Bqnr6quv09y5rysUCmn+/Ld16613yuFwHPY1t9xyh2655Q5Tx/Htt9/EPz7mmGY688yzi3Wc7t0vVvfuF5s1LEOhUEjvvvuWpOhylGuuua5UzwckC0I2UA7Nnft6vCvdiSeerGnTHi/0Jiav16suXc5Rly7nKBQKFek8Dke08UxWVpZGjBhhWNOwYUM98EB07Spb9iHV1atXX+edd4Hef/9d7d27RwsXLtCFF/7jyC802cEh+8Ybby1xJ8bStGjRx9q5c4ck6ZxzzlPDho0TOyCgjLBcBCiHli9fEv/40kuvOOpdAmw2W5HOE9uyb9KkSdqxY4dhzfjx4+V2u5WXR+MZlA8333y77PboHNVLL72oSALu4o2F7CZNmuqss84t8/MXxezZ0d2GbDab6TP6QDIjZAPl0K5du+Ifx2aQzBZrPPP777/r4YcfNqzp1KmTevbsqXA4ouxsZrFRPtStW09XXx1d8rBly0/68MOi3yxcEvv379NPP22SlAqz2B9pw4boDY+XX361GjZslOARAWWHkA2UQz5fWvzjZ5556pAubuadIzqLPWzYMOXk5BjWTJs2TZKUl+en8QzKlZtuuk01atSUJD377FOHbMdX2ipVytDnny/XF1+s0Lnnnl9m5y2qYDCof/3rSUlSlSpVdeutdyZ4REDZskQS8T6XSfz+oPbty030MI5ajRrpkqRduw4keCQoqWS/li+++IKeeeapQx5r1KixzjnnPJ166ulq1apNiWa/vF6nfD6XVq5cqY4dOxq+XX7ZZZdp7ty5CofD2rMnO6n3xU7264nDC+XkKP+Xn5W/9Xd5bRGFg0Hl5odkcbvlqltProaNZGM3i5TE72b5karXMiPDI6ezeLcwErLLUKr+gKGgZL+WwWBQY8aM0Mcff2j4fLVq1XXGGV10wQUXqV2744p0bIvFoqpVvbJarTrnnHP0ySefFKhxOBxavXq1mjdvrgMH8pSXl9z7Yif79cShIuGwctb+qP1ffqG8zT8pUMj9AAdz1Kold5OmqnTq6fK2LtkfmSg7/G6WH6l6LQnZKSJVf8BQUKpcyy+//EKvvvqyVq78utCdQ044oaMGDx6hevXqH9Ux09Jc8niceuedd3TxxcZbf917772aPn26gsGQ9u41XkqSTFLlelZ0oZxs7V/8hTIXfaLAju3FPo6jVm1VPutsVTrtdNm8PhNHCLPxu1l+pOq1JGSniFT9AUNBqXYt9+/fr2++Wa6lS5fo888XKTNz7yHP165dR7Nnvya3233Y49hsVlWp4lUoFNKxxx6rtWsLdpKsXLmyNm7cqGrVqmnfvhz5/UXbFjARUu16VkQHVizTztkvKpSVZdoxbWlpqtmrt9I7nWTaMWEufjfLj1S9liUJ2dz4CFQAlSpV0llnnatBg4bprbcWaNSoh1SzZq3489u3b9MXX3x6xOPEGs8888wzhgFbit4IWa1aNfn9wZQI2Ehuwf37tfXpJ7RtxlOmBmxJCmVladuMp7R1xpMKHthv6rEBgJANVDBWq1XnnXeBnnrqufhev9KRt/qLNp6xa//+/XrwwQcNa5o0aaJ7771XktiyDyWWt/kn/TxquLK+XlGq58lasVw/jxyuvC2bS/U8ACoWQjZQQdWuXUe1a9eJf165cpXD1qelRbfsmzBhwiH7cB9swoQJcrlcNJ5BieWsX6dfp05SqIxmmEMH9uvXqZOUs35dmZwPQPlHyAbKkaLcYvHzz1v0+++/xT8/9tj2hda6XHbZ7Tb9/PPPevTRRw1rTjnlFF177bU0nkGJ5W3+Sb8/9rAi+WX7cxTJy9Pvjz3MjDYAUxCygXJi375M9ep1tebNe1PZ2Ydfu/rLL1s0dGj/eCg/6aRT1KBBw0LrY41nhg4dqry8PMOaWNfH3Fwaz6D4gvv36/fpj5Z5wI6J5Ofr98ceYY02gBIr3u2SAJLO+vXr9PPPWzRlyng99thUdejQSe3aHacmTY5RRkaGcnJytGPHdi1b9pUWL/5c4XB0OUeVKlU1YMDQQo/r9Tpls1m1fPlyvfLKK4Y1V111lTp37qxQKKzcXH+pfH2oGHa+PKvMlogUJnRgv3a+NFt177w7oeMAkNoI2UA5sWHD+vjHfr9fS5Z8qSVLvjzsaxo1aqwJE6aqTp26hs9brRZ5PE5JUr9+/QyXozidTk2aNEmSlJPjT+rOjkhuB1YsU9aK5YkehiQpa8UyHVhxotI7nZjooQBIUSwXAcqJDh066aqrrlXjxk2O2M2uXr36uvvu+/Wf/7yihg0bF1rn9TpltVo0d+5cff7554Y1//znP9W0aVMFg6Gk7+yI5BXKydbO2S8mehiH2Dl7pkI52YkeBoAUxUw2UE60atVarVq1liRlZWVp48b12rr1d2Vm7pXf75fX61XVqtXUokUrNWzY6IjHs9mscrsdCgQCGjRokGFN1apVNXz4cEls2YeS2b/4C9P3wS6pUFaW9n+5WFW6np/ooQBIQaaE7FAopFdeeUVz587VTz/9pFAopAYNGqh79+669dZb5XK5zDgNgKOUlpam44/voOOP71CCY0Qbzzz99NPasGGDYc2IESNUpUoVGs+gRCLhsDIXfZzoYRjK/ORjVT73vCO+OwQAf1fikB0KhXT33Xdr0aJF8nq9at++vex2u1atWqXp06fr008/1cyZM+XxeMwYL4Ay4HDY5HTalZmZqTFjxhjWNGvWTPfcc48ikYiyspjFRvHlrP1RgR2Hb4aUKIEd25W79kd5W7dJ9FAApJgSr8l+7bXXtGjRIrVs2VLvv/++/vOf/+i5557TggULdMIJJ2jVqlV66qmnzBgrgDISazzz0EMPaffu3YY1EydOlMPhUF5eQKEQjWdQfPu//CLRQzisfUk+PgDJqcQhe+7cuZKi++fWqlUr/njVqlXjrZfffffdkp4GQBlxux2y223avHmznnjiCcOa008/XVdeeaXC4YhyctiyDyWTt/mnRA/hsPJ+Su7xAUhOJQ7ZVapUUdOmTXXccccVeK5x48aSpJ07d5b0NADKgMUS3VFEkgYPHqx8g4YgFotF06ZNk0TjGZRcKCcnaZeKxAR2bFcoJyfRwwCQYkq8JnvGjBmFPvf9999LkmrXrl3S0wAoAx5PtPHMkiVL9OqrrxrW9OjRQyeddJJCoTCz2Cix/F9+TvQQjkr+Lz/L++fuPQBwNEptn+xIJKLp06dLks4/n+2PgGR3cOOZvn37Gta4XC5NmDBBkpSTw82OKLn8rb+bejxH5cryNmxg6jEl88cJoPwrtX2yH374YS1btkzVq1fXrbfeWirncDrtqlEjvVSOXZpSccwwVh6v5WuvvaavvvrK8Ln7779fjRpF99hOT/covZx9+eXxeia7fJt5y41qnddVjW++UTa3S8tvvFWBfftMO7bXzs9HIvG9Lz8q0rUslZD92GOP6ZlnnpHT6dSjjz6qqlWrlsZpAJgoEokoEAho8ODBhs9Xr15dQ4cOLeNRobwLB4MlPoazahUdc89dqtqpY/wxm8dtasgOB+hmCqBoTA3ZwWBQY8aM0Zw5c+RyufT444/rxBNPNPMUh/D7g9q3L7fUjm+22F9vu3YdSPBIUFLl7VpmZHjkdNr1+OOP66dCdlIYNWqUMjIylJ8f1P79qfN7dzTK2/VMJbn5JWtiVP2M09X0jlvlSE/Xnj17lJaWJqfTqVBunkkjjMr1h/n5SAB+N8uPVL2Wsf8/Fodpa7Kzs7N15513as6cOapUqZKef/55denSxazDAyglTme08cyePXs0btw4w5qWLVvqzjvvVCQSoX06TGVxu4v1Ont6uloO6KeW/R+QIz1d8+fPV7t27RT4c8Y5ZLAzTklY6FwMoIhMmcnet2+fbrrpJq1evVp16tTRM888oxYtWphxaAClzOeLhocxY8Zo7969hjWTJ0+W3W5Xbq6fxjMwlatuvSK/psqJndTsnjvlrFJFBw4cUN++ffXcc8/JYrHI5/NJksImh+zijBNAxVbikO33+3X77bdr9erVatasmZ5//nm27ANSRKzxzIYNGwrtzHrWWWfpkksuUTgcVnY2W/bBXK6GjY661ub1qsmtN6nWuedIkj799FPdeOON2rJliyTJ6/VKkkJ5eVLE3P3bizJOAJBMCNnTp0/Xt99+qzp16mjWrFnc5AikiIMbzwwaNCj+NvuhNQc3ngkoYnJwAWxerxy1ah2xIU3Gcceq2b33yF2zhvLy8jRkyBA99thjh/xMxmaxQ3nmrsd21Kot258BHgCOVolCdmZmpmbNmiUp2kZ9/PjxhdZOnTq1JKcCYDKvN9p45vPPP9fcuXMNa3r16qUOHTrQeAalyt2kaaEh2+p0qlGfG1T3H90lScuWLVOfPn20du3aArVpaWmSpHCeuUtF3E2bmno8ABVDiUL2d999p7w/ZwxWr16t1atXF1pLyAaSh9VqkdsdncXu16+fYY3H44n/4czNjihNlU49XQeWFNybPb1lCzW//1556tVVIBDQmDFjNGHCBIVCxjuSlNZMdsapp5t6PAAVQ4lC9plnnql169aZNRYAZcTnc8lqteiVV17R8uXLDWseeOAB1a9fX4FASPn5Jd/LGCiMt1VrOWrVVmDHdkmSxW5Xw+uuVb3LL5XFZtP333+v3r1769tvvz3scWIz2WaGbEft2vLQTh1AMZRaW3UAyclut8rtdsTXtRqpVatWvCkNs9gobRarVZXPOluS5GvSWO2nTVb9q65QWNLEiRPVqVOnIwZs6a+Z7LCJIbvyWefIYrGYdjwAFUeptVUHkJxiW/Y99thj+vnnnw1rRo8erfT0dOXnBxUIlKxZCHA0Kp12ujwOi+pdfqmsdrs2bNigPn366KuvCi4jKcxfM9nm/GFoS09XpVNPM+VYACoeZrKBCsTptMvptGvXrl2F3qjcpk0b3XrrrTSeQZmx2ayqVreGGlx9pax2u5544gkdf/zxRQrY0sFrss3pSFqzZ2/ZvD5TjgWg4mEmG6hAfL7ozY4PPvig9u/fb1gzZcoU2Ww2Gs+gTHg8Dnm90XsEfv31V91000366KOPinUsM3cXSet0ktI7nVji4wCouJjJBioIjyfaeGbt2rV65plnDGu6du2q7t2703gGpc5qtSgjw6O0NLesVov+85//6Nhjjy12wJbM213Ell5JNXv2KtExAICZbKACOLjxzMCBAxUMFtwtxGq1xhvP5OTQeAalKyPDK7s9Os/Tq1cvvfTSSyU+ZnwmuwQt1S1ut+rd/4Ds6ZVKPB4AFRsz2UAFEH073qpPPvlEb7/9tmFNnz59dNxxxykUCis3l1lslC6//68/9KZNm6Y77rhDNputRMeMz2TnFm9NtsXtVr37HpC7cZMSjQMAJEI2UO5ZrRZ5PA5JUv/+/Q1rfD6fHnroIUls2YeykZ2dr717sxUIhFSrVi3NmDFD3333nbp3717sY8Z3FynGTLYtvZIa9B8kb4uWxT4/AByMkA2Ucz6fSxaLRS+++KK++eYbw5r+/furbt26NJ5BmQoGw8rMzNG+fbkKhcJq06aN3n33XX344Ydq06ZNkY/310x20dZkp3U6SY3GPMQMNgBTsSYbKMdijWdyc3M1bNgww5o6depowIABkqSsLGaxUfb8/qD27An+udOIU127dtXbb7+tY445pkjH+WtN9tGFbFt6umr27M0uIgBKBSEbKMfS0tySomtef/vtN8OasWPHyufzKT8/oGCQxjNInNzcgGw2qzwep1atWlXk1/+1u8jh/1h01Kqtymefo0qnnsY+2ABKDSEbKKecTrscDpt27NihSZMmGdYcd9xxuummmxSJRJjFRsLZbNF3XgKBgAYNGlTk1/+1T3bBmWxHrdpyN22qjFNPl6dVa1qlAyh1hGygnEpLi7ZPHzlypLKysgxrpk6dKqvVqpwcv8JhtuxDYqWlRe8fmDFjhjZs2GBYc8IJJ8jlcmnJkiUGr4+G7OpnnSln63ayuFxy1a0nV8NGsnm9pTp2APg7QjZQDnk8DtlsVq1evVrPP/+8Yc0FF1yg8847T+FwWDk5zGIjsRwOm5xOuzIzMzV69GjDmmOOOUZfffWVXC6X3nvvPfXv319r1qyJPx9bLlKn2/my7zpQJuMGgMKwuwhQzhzceKZ///4KhQqus7bZbJo6daokKSfHL/rOINFi77yMGzdOu3fvNqyZOHGiXK5o3YUXXqjvvvtOM2bMUK1atf48RlrZDBYAjgIhGyhnYo1nPvzwQ73//vuGNbfccovatm37Z+OZQBmPEDiU2+2Q3W7Tli1b9PjjjxvWnHbaabrqqqsUDke0Z0+2cnP9slqtuuOOO7RhwwYNGzZM6enpZTxyACgcy0WAcsRmizaeCYfDhTaeSU9P15gxYySxZR+SQ+ydl8GDByvfoJGMxWLRtGnTJEm5uX6FQmFlZeUrNzcgn8+p9PT0eDMlAEgWzGQD5Uis8cy///1vfffdd4Y1AwcOVK1atRQIhA5pbQ0kgtfrlM1m1ZIlSzRnzhzDmmuvvVYnn3yyQqGwcnL88cdDobD2789TZmaOAgG2nwSQXAjZQDnhcNjkcjmUnZ2tESNGGNbUr19f/fr1kyRlZRWtKx5gNqvVIo8nOosd+7n8O5fLpQkTJkjSIQH7YIFAKN45EgCSBSEbKCd8vugNYVOmTNG2bdsMa8aNGyePx6O8vICCwXBZDg8oIHr/gEWvv/66vvzyS8Oa++67T40bN1YwGFJe3uHvH+CdGQDJhJANlAMuV7TxzNatWzVlyhTDmg4dOqh3796KRCLKzmYtNhIr2njGLr/fX2jjmerVq2vYsGGSuH8AQOohZAPlQGwWe/jw4crJyTGsiW3Zl5sboPEMEi7WeOaJJ57QTz/9ZFgzcuRIZWRkyO8PsuYaQMohZAMpzuOJ3ji2atUqzZw507Dm4osv1tlnn03jGSQFpzPaeGbPnj2F7grSokUL3XnnnYpEIsxiA0hJhGwghVksFnm9DknRxjPhcMF11na7Pb6EhMYzSAaxd17Gjh2rvXv3GtZMnjxZDodDeXkBhULcPwAg9RCygRTm8zlltVo1f/58LVy40LDm9ttvV8uWLRUMhmg8g4SLNZ7ZuHGjnnzyScOaLl266NJLL1U4HFF2tvGOIgCQ7AjZQIqK3jjmUCgU0oABAwxrKlWqpAcffFCSCCtIOIvlr8YzgwYNUiBQ8I++vzeeifDWC4AURcgGUlSs8cxzzz2nNWvWGNYMHTpUNWrUkN8fZHszJFzs/oEvvvhCb775pmFNz5491bFjxwKNZwAg1RCygRQUbTxj14EDBzRy5EjDmkaNGun//u//JIkt+5BwR9N4xuPxaPz48ZL4mQWQ+gjZQAqK3Tg2ceJE7dy507Bm/PjxcrlcNJ5BUvD5oo1nXnnlFS1btsyw5oEHHlCDBg0UCISUn887LwBSGyEbSDGxxjO//fabHnnkEcOaE088Uddffz2NZ5AU7Pbo/QP5+fkaOnSoYU3NmjU1ePBgScxiAygfCNlAionNYg8dOlS5ubmGNQ8//LCk6I1jNJ5BosV+Zh977DFt2bLFsGb06NFKT09Xfj6NZwCUD/ZEDwDA0fN6ozeOffPNN5o9e7ZhzeWXX67TTz/d8MYxh8OmtDRX/O14wgxKm9Npl9Np1x9//BFfb/13bdq00W233cY7LwDKFUI2kCIsFos8nmjjmX79+hlubeZwODRp0iRJxo1n7Har7Hab7HabPB6nwuGw8vODBG6Umtgs9ujRo7Vv3z7DmsmTJ8tmsyk310/jGQDlBstFgBQRazzz1ltvadGiRYY1d999t5o3b65gMKS8vIJ7EB98M1lmZqasVqs8HqcqV/aqalWf0tJccjhspfUloIKJNp6xat26dZoxY4ZhzbnnnquLLrpI4XCYvdwBlCvMZAMpINZ4JhgMauDAgYY1VapUiW/nV9hb7uFwRIFASA6HTe+995727duntm3bqm3btqpatao8Hqc8HqdCodgMNzuToHgslugfhpI0cOBABYMFdwuxWq3xxjM5OQEazwAoVwjZQAqINZ6ZMWOG1q1bZ1gzbNgwVa1a9c/GM4Uv/fD7g3I4bGrdurXmzZunHTt26OOPP1adOnXUtm1btWnTRlWqVJHX65TXS+BG8Xi9LlmtVi1atEhvvfWWYU2fPn3Uvn17hUJh5eYyiw2gfCFkA0ku1nhm3759Gj16tGFN06ZNde+99yoSiSgr6/A3juXnB+TzudSyZUtZrVaFw9HgvG3bNm3btk0LFy5U3bp11a5dO7Vp00YZGRl/C9wB5ecHCdwoVLTxTPT+gf79+xvWeL1ePfTQQ5LYsg9A+UTIBpJcWlr0xrHx48frjz/+MKyZOHGinE6n8vICR7xxLBSKKBgMyePxqEmTJtq0aVOBmq1bt2rr1q364IMPVL9+/fgMd6VKleT1uuT1uhQM/hW4uVkNB4u98zJr1ix9/fXXhjX9+/dX3bp1aTwDoNyyRFJ4EZzfH9S+fcb7BCejGjXSJUm7dh1I8EhQUmV1Ld1uu9LTPdqyZYtatWql/PyCM36dO3fWl19+qXA4or17s49qX2yv1ymfz6VvvvlGb7/99lGPp2HDhmrXrp1at26ttLS0+OPBYCi+S0kqBm5+N81jt1tVpYpPubm5atmypX799dcCNXXq1NGGDRvk8/mUmZlj6s42XMvyhetZfqTqtczI8MjpLN6cNDPZQBLzeqOz2EOGDDEM2JLiN44VpfFMfn5QPp9LrVq10rvvvhtfMnIkv/zyi3755Re99957atSoUTxwe71e2e02+XyueODOywvQCKcCSktzS5IeeeQRw4AtSWPGjJHP51N+foCtIwGUW4RsIEnFGs8sW7ZMc+bMMay55ppr1Llz5yLfOBYKhRUMhuT1etWoUSNt3ry5SGOLRCLasmWLtmzZovnz56tx48Zq166dWrVqJY/HI7vdJqfTrszMnCIdF6nN6bTL4bBpx44dmjhxomHNscceq5tvvpnGMwDKPfbJBpJQ9Max6PZnffv2NdzazOVyxYOMUeOZI4mtg23Tpk2JxhoOh/XTTz/prbfe0ocffnjQ8Qvu043yLdZ4ZtSoUTpwwPgt4alTp8pqtSo3N6BQiHc6AJRfhGwgCXm9TlmtFr3xxhtavHixYc0///lPNWnSpNDGM0cSC9mtW7eWxWIp0XglqX379rr44oslRXeLyM0lZFckHk+08cyaNWv03HPPGdZccMEFOv/88xUOh5WTw5Z9AMo3QjaQZGKNZwKBgAYPHmxYU61aNQ0fPlySjrhlX2GiS0bC8vl8atSoUbHHK0nHH3+8Lr30UlksFmVl5ROgKhiLJfqHoSQNGDBAoVDBddY2m01Tp06VFHvnhVlsAOUbIRtIMmlp0e3PnnzySW3cuNGwZuTIkapcubL8/mCJbhzz+6OzzSVZMnLCCSccErBpKlLxxBrPLFy4UPPnzzesufnmm9W2bds/7x/gXQ4A5R8hG0giTmf0hsG9e/dqzJgxhjXNmzfXXXfddVSNZ44ktmSkVatWxVoycuyxx+qSSy6RJGVl5RGwK6BY45lwOFxo45m0tDSNHTtWEo1nAFQchGwgicRuHBs7dqz27t1rWDNp0iQ5HI6jajxzJMFgWKFQWOnp6WrQoEGRXx+bAQ8GmZ2sqGLvvMycOVOrVq0yrBk0aJBq1apF4xkAFQohG0gSbrdDdrtNmzZt0pNPPmlYc+aZZ+ryyy9XOBwxbd1zSXYZWbhwobKysmS3W5WR4TFlPEgddrtNLpdD2dnZ8XsE/q5evXrq16+fpOi7HQBQURCygSRw8I1jgwcPlt9fMEBbLJZiNZ45kthWe61bty7ya3fv3q2ZM2cqKytLTqedoF3BpKVF33mZOnWqtm7dalgzbtw4eTwe5eUFFAymXjdQACguQjaQBDyeaOOZL7/8Uq+//rphzXXXXadOnTopFDJ3+7PYkpFKlSqpfv36RX79H3/8oZkzZyo7O5ugXYG4XNHGM9u2bdOUKVMMa0444QT16dOHxjMAKiRCNpBgBzeeib2t/ndut1sTJkyQVDo3jpW0Mc3fg3alSgTt8i52/8CIESOUnZ1tWPPXOy8B0955AYBUQcgGEsznc8lqtWjOnDlasmSJYc3//d//qWHDhgoGS+fGsSMtGTn55JM1cOBAde7cudBj7Nq1Sy+++KJycnLkchG0yzOPxyGbzarvvvtO//73vw1r/vGPf+jss8/+s/EMs9gAKh5CNpBAdnu08Ux+fn6hjWdq1KihIUOGSCp+45kjiS0ZqVy5surWrXvIc6eeeqouuOACeTwenX/++Tr11FMLPc7OnTsJ2uWcxWKJ3z/Qv39/hcMF11nb7fb4EpJo45kyHSIAJAVCNpBAsbfcp0+fri1bthjWPPjgg6pUqZLy80vWeOZIjJaMnHbaaTrvvPMUiUSUlxdQJBLReeedp1NOOaXQ4+zYseNvQdtdamNG2fP5nLJarXr//ff14YcfGtbcfvvtatWqlYLBEFs7AqiwCNlAgsQaz+zevVvjx483rGnVqpVuv/32MrlxzO8/NGSffvrp6tq1659Nb/J04EBefCa9W7duOvnkkws91o4dOzRr1izl5ubK5XIQtMsJm80it9uhUChUaOOZSpUq6cEHH5QkZWfTnAhAxUXIBhLE54sGz9GjRyszM9OwZsqUKbLb7aY0njmSQCCkUCisKlWq6LLLLtO5556rSCSiAwfylJcXDeB5eQEdOBDd6/iCCy7QSSedVOjxtm/fTtAuZ3y+aOOZ559/XqtXrzasGTJkiGrUqKFAIBj/ww0AKiJCNpAA0cYzVq1fv14zZswwrDnnnHP0j3/8Q+FwuMxmBGOhqH379vGA/fcbLQ8O2hdeeKFOPPHEQo+3bds2zZo1S3l5eQTtFOdwRBvPZGVlaeTIkYY1jRo10v/93/9JKr37BwAgVRCygTJmsUTXtUrRdtOBQME1q1arVVOnTpUk5eRE10KXhVigLixgxxwctLt3765OnToVesy/B+30dIJ2KordPzBp0iTt2LHDsGbcuHFyu900ngEAEbKBMuf1Rm8c++yzz/S///3PsOaGG27QCSecoFAorNzcslvXGgiElJWVp337co+4VeDBQfuiiy5Sx44dC63dunWrZs+erfz8fLndBO1UE2s889tvv8X3vv67E088UT179lQ4TOMZAJAI2UCZOrjxTN++fQ1rvF6vxo0bJ6l0Gs8cSW5u4Kh3MTk4aP/jH/9Qhw4dCq39/fffCdopKjaLPWzYMOXm5hrWxMJ3Xp6fxjMAIMme6AEAFUnsxrHZs2fr66+/Nqzp27ev6tWrp0CgdBrPmC0vLyCLRUpLc+viiy9WJBLRypUrDWt/++03zZ49W7169ZLbHQ1usZCO4gsGg1q58mutWrVSa9eu0W+//ao9e/YoPz9Pbrdb1avXUKtWbdS1azd17nxakY7t9Tpls1m1cuVKzZo1y7Dm8ssv1xlnnPFn4xl2FAEASbJEymqxZynw+4Pat894ViUZ1aiRLknatetAgkeCkirOtbTbrapSxae8vDy1bNlSv/zyS4Ga2rVra8OGDUpLS1NmZk6p7ottNo/HobQ0tyKRiN566y19++23hdY2aNBAvXr1ktPpPGQ2PFFS+Xfzk08WatKkccrKOrqxn3TSKRozZqLS0tKOWGuxWFS1qldWq1XnnHOOPvnkkwI1DodDq1evVvPmzf/ciSax+2Kn8rVEQVzP8iNVr2VGhkdOZ/HmpFkuApSRtLTozO0jjzxiGLAlacyYMUpLS1N+/tEv2UgWubkBZWXlyWKx6JJLLlH79u0Lrf3111/10ksvye/3s3SkhL76avEhAbty5Spq3bqNOnY8Se3bn6CaNWsdUr9s2RKNGDHoqI4dazzz9ttvGwZsSbrrrrvUvHlzBYOhhAdsAEgmLBcByoDTaZfDYdfOnTs1YcIEw5p27drp5ptvLpPGM6Ul2t3PorQ0ly699FJFIhF99913hrW//PKLXn75ZV1//fVyu52KRKSsLJaOFNXmzT/pnHPO02mnnaGOHU9S9erVC9Rs2bJZM2Y8ri+++EyStHz5Un399XJ17Fj49os2m1Vut0PBYFADBw40rKlcuXJ8O79U/ZkFgNLCTDZQBmJb9o0aNUoHDhi/VTZlyhTZbDbl5gYUCqXsKi7l5vqVlZUvi8Wiyy67TMcee2yhtT///LNefvllBQKBP5ebuMpwpOXDY489pTFjJqhbt+6GAVuSGjduovHjp6pdu+Pijy1d+uVhjxu7f+CZZ57R2rVrDWuGDx+uatWqye8Pyu9PrXdeAKC0EbKBUubxOGS32/Tjjz/q2WefNaw5//zzdcEFF5SbG8dyc/3Kzv4raLdr167Q2kODtpOgXURer++o6qxWq0477cz454XtdS3FGs/YtX///niL9L9r0qSJ7r33XknMYgOAEUI2UIoslujuDJI0YMAAhUIFZ/sObTzjL7PGM6UtJycatK1Wqy6//HK1bdu20NotW7bolVdeIWiXspyc7PjHNput0LrY93/8+PHatWuXYc3EiRPjN67SeAYACmJNNlCKvF6XrFarPvroI7377ruGNTfddJOOPfbYPxvPlK8bx2Kz8j6fS1dccYUikYjWrFljWLt582b997//1XXXXRffS5zW3Edvw4b1+vHH1frpp03av3+fsrKyFAweugXkpk3r4x9XrVrN8Dgul112u00///yzHnvsMcOazp0765prrqHxDAAcBiEbKCXRxjMOhcNh9e/f37DG5/Np7NixksrvW+4HB+0rr7xSkUhEP/74o2HtTz/9pP/+97/q0aMHQfsohEIhzZv3pt54Y45+/nlLkV7bsGEjw8djjWeGDh2qvDzjG1FjjWdyc2k8AwCFYbkIUErS0qI3jr344ouF7hk9cOBA1alTJ2UazxTXwUtHrrrqKrVu3brQ2k2bNmnOnDkKBoPyeJzx0IdD7dy5Q7fd1lsPPzypyAFbko45pnmBx2KNZ5YvX65XXnnF8HVXX321Onfu/Oc7L6l//wAAlBaa0ZShVN2IHQUd6VrGGs/k5OSoefPm2rp1a4GaevXqaf369fJ6vdq7N7tCrGv1+Zzyel0KhUJ6/fXXC921QpKaNWuma6+9Vna7PR7SS0uq/W7u3btXt956g3bs2B5/rEOHTjr99C5q3bqN6tSpK58vTW63WxaLRZL09dfLdf/9d0mKrsf+4IPP5HL99QeM1WpRlSrRxjNnnnmmPv/88wLndTqd+vHHH9W0adOkaDxjJNWuJQ6P61l+pOq1LEkzGpaLAKUgLS3aXGXq1KmGAVuSxo4dK6/Xq/z8inPjWHZ2dObT63Xpqquu0muvvaZ169YZ1m7cuFGvvvqqrr322vjNo+V1SU1RPfro5HjArly5ssaMmagOHTod9jUrV34d/7hx46aHBGwpOotttVo1d+5cw4AtSffee6+aNm1K4xkAOAosFwFM5nLZ5XDYtH37dk2ZMsWwpn379urTp48ikUiFW3Ocne1XTo5fNptNV199tVq0aFFo7YYNG/Tqq68qFArJ62XpiCT98ccf+uSTj+KfDxo0/IgBW5IWL/4s/nHLlq0OeS7WeCYQCGjQIONukFWrVtXw4cMl8ccOABwNQjZgslgQHDFihLKysgxrpk2bJqvVqtzcQIW8cSw7Oz8etK+55ho1b15wfXDM+vXr9dprrx0UtJ1lONLks2LFUoXD0Xc+MjIydPrpXY74mlWrvtWGDX/tLPL3kB27f+Cpp57Shg0bDI8xcuRIVa5cmcYzAHCUCNmAiTweh2w2q77//nu98MILhjXdu3fXueee+2fjmYo7I/j3oN2sWbNCa9etW6fXX3/9z6DtqtBBe9eunfGPK1XKiK+5LkwoFNJjj0095LEWLf4K2Q6HTU6nXZmZmfGdbv6uefPmuvvuuyvkOy8AUFyEbMAkFovlkMYzsdnGg9lstvgSkmjjmTIdYtKJBW273a5rr71WxxxzTKG1a9eu1RtvvKFwOCyv1xX/Xlc0B4fqbdu2yu8//A4fDz88SevX/3WDqc1mU/PmLeOfxxrPPPTQQ9q9e7fhMSZOnCiHw6G8vIBCoYpx/wAAlBQhGzBJ7MaxBQsWaMGCBYY1t912m9q0aaNgsPw1nimu7Ox85eZGg3aPHj3UtGnTQmt//PHHeND2+Spm0G7a9K8Z/2AwqH//+1nDugMHDujBB4dp3rw3D3m8YcNGcrujN+a63Q7Z7TZt3rxZjz/+uOFxzjjjDF1xxRUKhyPxPc8BAEfG7iKACWy2aOOZUChUaOOZ9PR0jR49WhI3jv1dbAmCx+NUjx499Morr2jz5s2GtWvWrJHFYtEVV1wRX/9ekcJfx44nqnr1Gvrjj2i781mz/q2fftqoc845TzVr1tL+/fu1atU3ev/9+dq/f59q1qylhg0bacWKZZL+WipisSj+R8rgwYMNZ8QtFguNZwCgmAjZgAl8vuiNYy+88IJ++OEHw5rBgwerZs2aCgSC8vvLb+OZ4jo4aF933XWHDdqrV6+WxWLR5ZdfXuGCtsvl0sCBwzR4cN/4kqTFiz/X4sUFt91r0qSpJk58WCNHDok/1rJltBGQxxNtPPPVV1/p1VdfNTzXddddpxNPPFGhULjCfH8BwCwsFwFKyOGwyeVyKCsrSyNHjjSsadCggR544AFJtAk/nKys6NIRh8Oh6667To0bNy609ocfftD//ve/Crl05NRTT9fkyY+qVq3ahs/XrFlLd9xxj/7975dVq1Zt/fTTxvhzLVu2ktVqibet79evn+Ex3G63xo8fL0kV+gZdACguZrKBEorNpE6ePFnbt283rBk/frw8Ho/y8ipO45niOnhG+/rrr9dLL72kn3/+2bD2+++/l8Vi0WWXXSafz6VIRBWm1fcpp5yqOXP+p5UrV+innzYpEAioWrXqatiwsdq0aXvIDZKffPLVIa/1+VyyWi169dVX9dVXX/390JKk+++/X40aNfqz8QzvvABAUdFWvQylaktRFBS7lvv356pSJY9+//13tWjRQjk5OQVqO3bsqBUrVigcjmjv3mzWtR6ltDSXPB6n/H6/XnrpJf3yyy+F1rZv316XXnqpLBZLfDa8KCrS76bdblXlyl4FAgG1bt1aP/30U4GaGjVqaOPGjapUqZIyM3MUCKTOvtgV6VpWBFzP8iNVr2VJ2qqzXAQogdgs9vDhww0DtqT4jWN5edw4VhRZWfnKywvI6XSqZ8+eatCgQaG1q1at0ltvvaVIJPJnOHeU4UhTS+z+gccff9wwYEvSqFGjVKlSJeXnB1MqYANAMiFkAyVgs1n17bff6sUXXzR8/tJLL1WXLl3+bDxTMZYxmOnAgbyjDtrffvut3n77bUlSWpqboG3A6Yw2ntmzZ48eeughw5pWrVrpjjvuUCQSYRccACgBQjZQTLGVVv369TNsPONwODR58mRJUnY2jWeKKxa0XS6Xevbsqfr16xdau3LlSoL2YcTeeRkzZowyMzMNayZPniy73U7jGQAoIUI2UEwWi0XvvPOOPv74Y8Pn77jjDrVo0eLPG8doPFMSBwftXr16qV69eoXWfvPNN3rnnXckEbQPFms8s2HDBj311FOGNWeffbYuvvhihcNhZWfzzgsAlAQhGygim82qSCSiYDCogQMHGtZkZGRo1KhRkmg8Y5a/B+26desWWvv111/r3XfflRQN2m53xQ7aFovk80W37Bs0aJACgYJ/9B3aeCagFL4nHgCSQqmE7DfffFMtW7bUihUrSuPwQELFbhx79tln9eOPPxrWDBs2TNWrV5ffH5Tfz41jZokFbbfbrRtuuOGwQXvFihWaP3++JCk9vWIHba/XKavVqs8//1xz5841rLnhhht0wgkn0HgGAExiesheuXKlxo4da/ZhgaQQbTxj1/79++Mz1X/XuHFj3XfffZKYxS4NBw7kKT8/GrR79eqlOnXqFFq7fPlyvffee5IqbtC2Wi1yuw/feMbj8WjcuHGS+JkFALOYGrI/+OAD3XLLLYVuZQakutiNYxMmTNCuXbsMayZMmCCXy0XjmVK0f380aHs8Ht1www2qXdu486EkLVu2TO+//76kihm0Y41nXn75ZS1fvtywpl+/fqpfv74CgZDy82k8AwBmMCVkb9++XQMHDtS9996rcDis6tWrm3FYIKm4XHY5HDb98ssvevTRRw1rTj75ZPXo0UPhMNuflbaDg3bv3r0PG7SXLl2qBQsWSKpYQdtut8rtdigvL09Dhw41rKlVq5YGDRokiVlsADCTKSH70Ucf1bx589SuXTvNmTNHTZs2NeOwQFKJzWKPHDlSeXl5hjUPP/ywpGhrbxrPlL6/z2jXqlWr0NolS5bogw8+kBTtJul2F6+DVyqJ/cw+9thjhbamHzNmjNLS0mg8AwAmMyVkN23aVJMmTdJrr72mli1bmnFIIKlYrRZZrRZJ0VDSs2dPWSyWQ2quvPJKnXrqqQqFwkVu643iiwbtoLxer3r37q2aNWsWWvvVV1/pww8/lMViUVqaWy5X+Q3aTqddTqddu3bt0vjx4w1r2rZtq1tuuYXGMwBQCiyRUtin6YYbbtCyZcv00ksvqVOnTmYfHkgKK1asUL9+/fTZZ5/J6XRqzZo1OuaYYxI9rAovOztbM2fOLHTNvCSddtpp6tq1qyKRSIE/lsqL2Nd2zz33FLov9vz583XhhReW8cgAoGJgn2ygGCKRiDp16qRPP/1Uc+fO1fjx4wnYScLn86lPnz6qUaNGoTWLFy/WRx99JIvFUm73g7ZYLFq7dq2eeeYZw+fPO+88XXjhheX26weAREvp90r9/qD27ctN9DCOWo0a6ZKkXbsOJHgkKKnYtQyHI7rsssvij+/bl8O+2AmWkeGRz+dT7969NXPmTP3xxx+GdV988YUsFovOOeec+KxvefjdtFikqlV9slqtGjhwoILBgruFWK1WTZ06VZKUne0vV8ub+He2fOF6lh+pei0zMjxyOosXl5nJBkpg795s5eb6FYlElJ8fIGAngX37cuX3B5WWlqY+ffqoWrVqhdZ+/vnnWrRoUXxGuzys0fZ6XbJarfrkk0/09ttvG9bcdNNNOu6447h/AABKESEbKIFwOKKsrHzt3p2l/fuNdxxB2StK0P7000/16aefymKxKD09tW+GtFot8nii2xMW1njG5/PFG4ZxsyMAlB5CNmAClrUmn1jQTk9PV58+fVS1atVCaxctWqTPPvssHrSL+9Zgovl8LlksFr344otauXKlYc2AAQNUp04dGs8AQCkjZAMot4oStD/55BN9/vnnslgsqlQp9YJ2rPFMbm6uhg0bZlhTt25dDRgwQJKUlcUsNgCUJkI2gHItFrQrVaqkPn36qEqVKoXWfvzxx/EbIlMtaKeluSVJ06ZN02+//WZYM3bsWHm9XuXnBxQMcv8AAJQmQjaAcq8oQfujjz7S4sWLUypoO512ORw27dixQ5MmTTKsad++vW688UZFIhFmsQGgDBCyAVQI+/blKhAIKiMjQ3369FHlypULrV24cKG+/PLLg4K2rewGWgxpadH26SNHjlRWVpZhzdSpU2W1WpWbG1A4zE0EAFDaSiVkz5o1S+vWraPbI4CkEg3aoXjQzsjIKLT2ww8/1FdfffVn0PYkbdD2eByy2axavXq1nn/+ecOa7t27q2vXrgqHw8rJYRYbAMoCM9kAKoxIJNowKBAIqXLlykcM2h988IGWLFmStEHbYpG8XqckqX///gqFCq6zttlsmjJliiQpJ8fPTjgAUEYI2QAqlIODdpUqVdSnTx9VqlSp0PoFCxZo2bJl8aDtcCRP0I41nvnwww/1/vvvG9bceuutatOmzZ+NZwJlPEIAqLgI2QAqnKIG7ffee0/Lly+XxWJRRkZyBG2bLdp4JhwOq3///oY16enpGj16tCS27AOAskbIBlAhHRy0q1atqj59+ig9Pb3Q+vnz52vFihVJE7RjjWf+/e9/67vvvjOsGTx4sGrVqqVAICS/n8YzAFCWCNkAKqxY0JZ0VEH73Xff1ddff53woO1w2ORyOZSdna0RI0YY1jRo0EAPPPCAJCkrK68shwcAECEbQAV38I2A1apVU+/evZWWllZo/TvvvKNvvvkmoWu0fb7oln1TpkzRtm3bDGvGjRsnj8ejvLyAgsFwWQ4PACBCNgDEBQIhVa9eXX369JHP5yu07u2339bKlStltZZ90Ha5oo1ntm7dGt815O86duyoG264QZFIRNnZrMUGgEQgZAPAn/bty1EweHRB+6233kpI0I7NYg8fPlw5OTmGNVOnTpUkGs8AQAIRsgHgT5GIlJmZq2AwpBo1aqh3795HnNH+9ttv40Hbbi/doO3xOGWzWbVq1SrNnDnTsOaSSy7RWWedReMZAEgwe6IHAFRUH3zwvhYuNN7buCi6dr1A559/QcLPk8rn6tnz6vjnkUhEmZm5qlzZo5o1a6p3796aOXOm4axxJBLRW2+9JYvFovbt2ysjw6N9+6Ih3WwWi0Ver0NStPFMOFxwnbXdbtfkyZMl0XgGABKNkA0kyK+//qwRI8YedjeLIzlw4IBeffXlpDhPeTqXUdB+8cUXCw3a8+bNk8Vi0XHHHfdn0M4x/WZDn88pq9Wq+fPna+HChYY1d955p1q2bKlgkMYzAJBoLBcBAAOxoB0MhlSrVi3dcMMN8ng8hdb+73//0/fffy+r1aKMDK/sdvP+ebXZrHK7HQqFQhowYIBhTUZGhkaNGiVJ3OwIAEmAkA0AhTg4aNeuXVu9e/c+bNCeO3eufvjhB9ODdqzxzHPPPac1a9YY1gwdOlTVq1eX3x+k8QwAJAFCNgAcRiQSia+zrl27tm644Qa53e5Ca998802tXr36z6DtKXHQjjaesevAgQMaOXKkYU3jxo11//33S2IWGwCSBSEbAI4gHP4raNepU+eogvaaNWtktVpLHLRjW/ZNnDhRO3fuNKwZP368XC4XjWcAIIkQsgHgKBwctOvWrasbbrhBLperkNqw3njjDf34448lCtqxxjO//fabHnnkEcOak046Sddddx2NZwAgyRCyAeAo/RW0w0cVtF9//XWtXbs2HrRttqL9kxubxR46dKhyc3MNax5++GFJUm6un8YzAJBECNkAUATRoJ2jUCisevXqqVevXocN2q+99prWrVsnq9WqypWPPmh7vdHGM19//bVmz55tWHPllVfqtNNOUygUVk6Ov9hfEwDAfIRsACiicDiizMxo0K5fv7569uwpp9NZSG1Y//vf/5SXlyerNboV35FYLBZ5PH81nokYdJVxOByaNGmSJBrPAEAyImQDQDEcHLQbNGigXr16GQZtp9OpHj16yO12KxQKKzf3yDPOscYzb731lhYtWmRYc8899+iYY45RMBhSXh6NZwAg2RCyAaCY/h60/z6j7XQ61bNnTzVq1EihUFiZmTlHXDcdazwTDAY1cOBAw5oqVapoxIgRktiyDwCSFSEbAErg4KDdsGFDXX/99XI4HHI6nerVq5caNmx41AFb+qvxzIwZM7Ru3TrDmuHDh6tq1ap/Np4Jmf0lAQBMYE/0AAAg1cWCduXKXjVq1EjXX3+9bDabGjRoUKSAHWs8s2/fPo0ePdqw5phjjtE///lPRSIRZWUxiw0AyYqQDQAmODhoN27cWJKKFLAlKS0tukvJ+PHj9ccffxjWTJw4UU6nU3l5AYVCNJ4BgGTFchEAMMnB2/sFg6EiBWy32yG73aYtW7boscceM6w57bTTdNVVVykcpvEMACQ7ZrIBwEShUER79mQX+XVeb/SGySFDhig/3zhAT5s2TRKNZwAgFTCTDQAJFms8s2zZMs2ZM8ew5tprr9XJJ59M4xkASBGEbABIIKvVIo8nOovdt29fw8YzLpdLEydOlCQCNgCkCEI2ACSQ1+uU1WrRG2+8ocWLFxvW3HfffWrcuDGNZwAghRCyASBBYo1nAoGABg0aZFhTrVo1DRs2TJLYsg8AUgghGwASJC0t2njmySef1KZNmwxrRo0apYyMDPn9QQUCNJ4BgFTB7iJAAo0aNVR2u63Yrw8GQ2rbtl3SnKc8n8tsTqdNTqdde/fu1ZgxYwxrWrRooTvvvJPGMwCQgiwRo7tsUoTfH9S+fbmJHsZRq1EjXZK0a9eBBI8EJcW1LF8ScT2rVPHKbrepb9++euSRRwxr5s6dq8suu0y5uX5C9lHid7N84XqWH6l6LTMyPHI6izcnzXIRAChjscYzmzZt0pNPPmlYc+aZZ+qyyy5TOBxhRxEASEGEbAAoQxbLX41nBg8eLL+/YIC2WCx6+OGHJdF4BgBSFSEbAMqQxxNtPLN48WK9/vrrhjU9e/ZUx44daTwDACmMkA0AZeTgxjP9+vUzrHG73Ro/frwkKTubddgAkKoI2QBQRnw+l6xWi+bMmaOlS5ca1jzwwANq0KCBAoGQ8vODZTxCAIBZCNkAUAbs9mjjmfz8fA0ePNiwpmbNmhoyZIgkZrEBINURsgGgDPh8LknS9OnTtWXLFsOaBx98UOnp6crPp/EMAKQ6QjYAlLJY45ndu3fH11v/XevWrXX77bcrEokwiw0A5QAhGwBKmc/nliSNHj1amZmZhjVTpkyRzWZTXl5AoVC4DEcHACgNhGwAKEXRxjNWrV+/XjNmzDCsOffcc3XRRRcpHA4rO5st+wCgPCBkA0ApsVgkny+6Zd/AgQMVCAQK1FitVk2bNk2SlJMTUCRC4xkAKA8I2QBQSrxep6xWqz777DPNmzfPsKZ3795q3769QqGwcnOZxQaA8oKQDQCl4ODGM3379jWs8Xq9GjdunCS27AOA8oaQDQClwOdzyWKxaPbs2fr6668Na/r166e6devSeAYAyiFCNgCYLNZ4Ji8vT8OGDTOsqV27tgYOHCiJWWwAKI8I2QBgsrS0aOOZRx55RL/88othzdixY5WWlqb8/ACNZwCgHCJkA4CJnE67HA67du7cqQkTJhjWHHvssbr55ptpPAMA5RghGwBMFGufPmrUKB04cMCwZsqUKbJarcrNDSgUYss+ACiPCNkAYBKPJ9p45scff9Szzz5rWNOtWzd169ZN4XBYOTls2QcA5RUhGwBMYLFE98WWpAEDBigUKrjO2mazaerUqZKknBw/jWcAoBwjZAOACbxel6xWqz766CO9++67hjU333yz2rVr92fjmYLdHwEA5QchGwBKKNp4xqFwOKx+/foZ1qSlpWnMmDGS2LIPACoCQjYAlFBaWrTxzIsvvqhVq1YZ1gwcOFC1a9em8QwAVBCEbAAoAbvdJpfLoZycnEIbz9SrVy8+w52VlVeWwwMAJAghGwBKINZ4ZurUqdq6dathzUMPPSSv16v8/ICCwXBZDg8AkCCEbAAoJpfLLofDpu3bt2vKlCmGNccff7x69+6tSCSirCzWYgNARUHIBoBiijWeGTFihLKysgxrpk2bFm88Ew6zZR8AVBSEbAAoBo/HIZvNqu+//14vvPCCYc0//vEPnXPOOX82nmEWGwAqEkI2ABSRxWKJN57p37+/wuGC66ztdnt8CUm08UyZDhEAkGCEbAAoIq/XKavVqgULFuiDDz4wrLntttvUqlUrBYM0ngGAioiQDQBFYLNFG8+EQiH179/fsKZSpUoaPXq0JBrPAEBFRcgGgCLw+aKNZ1544QX98MMPhjWDBw9WjRo1FAgE5ffTeAYAKiJCNgAcJYcj2ngmKytLI0eONKxp2LChHnjgAUliyz4AqMAI2QBwlGJb9k2ePFnbt283rBk/frzcbrfy8mg8AwAVGSEbAI5CrPHM77//rmnTphnWnHjiierZs6fC4QhrsQGggiNkA8BRiM1iDxs2TDk5OYY1U6dOlSTl5flpPAMAFRwhGwCOwONxymaz6ttvv9WsWbMMay677DKdeeaZfzae8ZfxCAEAyYaQDQCHEW0845Ak9evXz7DxjMPh0OTJkyVJ2dk0ngEAELIB4LB8vmjjmXfeeUcff/yxYc2dd96p5s2bKxgMKS+PxjMAAEI2ABTKZrPK7XYoGAxq4MCBhjWVK1fWqFGjJNF4BgDwF3uiBwAAZeH441sV+TUzZ85U165d9eyzz+rHH380rBk2bJiqVasmvz8ovz9U0mECAMoJZrIBwMDpp5+url27av/+/fGZ6r9r0qSJ7r33XknMYgMADkXIBoC/sVqt8Y6OEyZM0K5duwzrJkyYIJfLReMZAEABhGwA+JurrrpKbdu21S+//KJHH33UsOaUU07RtddeS+MZAIAhQjYAHMTj8cRvchw6dKjy8vIM6x5++GFJUm4ujWcAAAURsgHgIHfccYfq1Kmj5cuX6+WXXzasufrqq9W5c2eFQmHl5tJ4BgBQECEbAP5Us2ZN3X333ZKk/v37K2LQVcbpdGrixImSpJwcGs8AAIwRsgHgT/3795fP59P//vc/ffbZZ4Y1//znP9W0aVMazwAADouQDQCSWrVqpR49eigQCBTaeKZq1aoaPny4JLbsAwAcHiEbACQNHz5cNptNTz/9tDZs2GBYM2LECFWpUoXGMwCAIyJkA6jwunTporPPPluZmZkaM2aMYU2zZs10zz33KBKJKCuLWWwAwOERsgFUaFarVSNGjJAkjRs3Trt37zasmzRpkhwOh/LyggqFaDwDADg8QjaACq1Hjx5q3bq1Nm/erMcff9yw5owzztAVV1yhcDiinBxmsQEAR2Y360BffvmlZsyYoXXr1ikQCKht27a6/fbbdcYZZ5h1CgCQJB1/fCtTjuP1ejVgwABJ0uDBg5WfXzBAWywWTZ06VZL0yCMPx5vQHI1vv11ryjgBAKnHlJnsN998UzfddJNWrlyp4447TieccIJWrlypW2+9VXPmzDHjFABgurvvvls1a9bUkiVL9OqrrxrW9OjRQyeddJK2b9+up59+uoxHCABIVSWeyd65c6dGjRql9PR0vfzyy2rRooUk6bvvvtNNN92kcePG6ayzzlKtWrVKPFgAMEudOnV05513SpL69u1rWON2uzVhwgRJ0pQpU5Sbm1tm4wMApLYSz2TPnj1bfr9fN954YzxgS9Jxxx2nW2+9Vfn5+cxmA0g6AwYMkMfj0WuvvaavvvrKsOa+++5To0aNtGbNmkJnugEAMFLikP35559Lkrp27VrgufPOO0+SCu2cBgCJ0LZtW1199dXy+/0aPHiwYU316tU1dOhQSdKYMWMUDrOjCADg6JUoZEciEW3cuFFWq1VNmzYt8Hzjxo1ltVq1ceNGRSKRkpwKAExzxx13yGq1asOGDcrLyzOsefDBB5WRkaGPP/44PpkAAMDRKlHI3rdvn/x+vypXriyn01ngebvdripVqig3N1fZ2dklORUAmGbx4sXy+/1q27atNmzYoNGjR8vn88Wfb9Wqle644w6FQiGNHTs2gSMFAKSqEt34GLsJyOPxFFrjdrslSdnZ2UpLSyvJ6QpwOu2qUSPd1GOWhVQcM4xxLVPTnDlztHTpUg0ZMkT/+Mc/NHLkSN1+++0aMWKEXnjhBU2aNEl2u12zZ8/W+vXri30efj4Sh+99+cL1LD8q0rUs0Uy21Xrkl7NMBEAy2rJli+644w5deuml+uabb1S7dm09++yzWrt2rS655BJlZWXF98cGAKCoSjST7fV6JcmwgUNM7LnDzXYXl98f1L59qbOlVuyvt127DiR4JCgprmX5sWLFCl188cW65JJLNGTIEDVv3lyS9NRTT2nXrl0lOjY/H2WP383yhetZfqTqtczI8MjpLF5cLlHITktLk9fr1d69exUMBmW3H3q4YDCovXv3yuVyqVKlSiU5FQCUqrfeeksLFixQ7969Vb9+ff3rX/9K9JAAACmsRCHbYrGoWbNm+u6777RlyxY1a9bskOc3b96scDh8yP7ZAJCs8vPz9eyzzyZ6GACAcqDE+2SfccYZkqSFCxcWeC72WJcuXUp6GgAAACBllDhkX3HFFXK5XHr22Wf1ww8/xB///vvv9dxzz8ntduv6668v6WkAAACAlFGi5SKSVL9+fQ0aNEhjxoxRjx49dMoppygSiWjp0qUKBoOaNGmSqlWrZsZYAQAAgJRQ4pAtST179lTdunX13HPP6euvv5bT6VSHDh101113qXPnzmacAgAAAEgZpoRsSTr77LN19tlnm3U4ACjUt9+uLfJrjj++VZmfEwBQcZV4TTYAAACAQxGyAQAAAJMRsgEAAACTEbIBAAAAkxGyAQAAAJMRsgEAAACTEbIBAAAAkxGyAQAAAJMRsgEAAACTEbIBAAAAkxGyAQAAAJMRsgEAAACT2RM9AAAoC99+u7bQ52rUSJck7dp1oKyGAwAo55jJBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATEbIBgAAAExGyAYAAABMRsgGAAAATGaJRCKRRA+iuMLhiILBUKKHcdScTrskye8PJngkKCmuZfnC9Sw/uJblC9ez/EjVa2m322S1Wor12pQO2QAAAEAyYrkIAAAAYDJCNgAAAGAyQjYAAABgMkI2AAAAYDJCNgAAAGAyQjYAAABgMkI2AAAAYDJCNgAAAGAyQjYAAABgMkI2AAAAYDJCNgAAAGAyQjYAAABgMkI2AAAAYDJCNgAAAGAyQjYAAABgMkI2AAAAYDJCNgAAAGAyQjYAAABgMkJ2Gdu4caMGDBigM888U+3atdMpp5yiu+++W99++22ih4YS8Pv9uuCCC3TjjTcmeigogi+//FK9e/fWySefrA4dOuiGG27Q559/nuhhoYTefPNNtWzZUitWrEj0UFAMoVBIs2fP1pVXXqkTTjhBxx13nC666CI9+eSTys/PT/TwUEShUEgvvviiLrnkEh177LE66aSTdPPNN2vRokWJHlqps0QikUiiB1FRLF26VLfddpvy8/N1zDHHqEmTJvrtt9+0du1a2e12TZkyRd27d0/0MFFEoVBI/fv31/z589W5c2f95z//SfSQcBTefPNNDRkyRE6nU6eccorC4bCWLl2qQCCgMWPG6Nprr030EFEMK1eu1M0336ycnBy99NJL6tSpU6KHhCIIhUK6++67tWjRInm9XrVv3152u12rVq3S/v371b59e82cOVMejyfRQ8VRGjhwoObNm6e0tDR17NhRgUBAy5cvVyAQ0H333ad77rkn0UMsPRGUCb/fHznrrLMiLVq0iMyaNeuQ5+bNmxdp2bJl5IQTTojs3r07QSNEcWRmZkZuv/32SIsWLSItWrSI9OnTJ9FDwlHYsWNHpF27dpGOHTtG1q1bF3981apVkQ4dOkSOPfbYyPbt2xM4QhTHggULIieccEL893H58uWJHhKK6JVXXom0aNEicvHFFx/yO7h79+7ItddeG2nRokVk6tSpCRwhiuLdd9+NtGjRItKtW7fIrl274o+vX78+0rFjx0irVq0imzdvTtwASxnLRcrIkiVLtHXrVnXq1Em9evU65LlLLrlE5557rrKzs/Xpp58maIQoikgkorfffluXXnqpFi1apAYNGiR6SCiC2bNny+/368Ybb1SLFi3ijx933HG69dZblZ+frzlz5iRwhCiK7du3a+DAgbr33nsVDodVvXr1RA8JxTR37lxJ0tChQ1WrVq3441WrVtWDDz4oSXr33XcTMTQUw1tvvSVJ6t+//yG/l82bN9fFF1+scDisxYsXJ2p4pY6QXUby8vLUrl07nXHGGYbPN27cWJK0c+fOMhwViuv3339X//79tXv3bt13330aO3ZsooeEIoitu+7atWuB58477zxJ0meffVamY0LxPfroo5o3b57atWunOXPmqGnTpokeEoqpSpUqatq0qY477rgCz/H/ydQzffp0vf322zrzzDMLPJednS1JstlsZT2sMmNP9AAqivPOOy/+P28j33//vSQd8pc7kpfD4dBVV12lu+66S/Xr19fSpUsTPSQcpUgkoo0bN8pqtRqGscaNG8tqtWrjxo2KRCKyWCwJGCWKomnTppo0aZIuueQSWa3MHaWyGTNmFPpc7P+TtWvXLqvhoIScTuch7xbGfPLJJ3r//ffl9XoNJzvKC0J2Evjqq6+0dOlSud1uw7/2kHxq1aqlcePGJXoYKIZ9+/bJ7/eratWqcjqdBZ632+2qUqWKdu/erezsbKWlpSVglCiK22+/PdFDQCmLRCKaPn26JOn8889P8GhQHHl5eRo4cKA2btyoTZs2qW7dupo8eXK5Xt7Fn/wJ9ttvv2nAgAGSov+jqFq1aoJHBJRvubm5knTY3Qncbrekv97OBJBYDz/8sJYtW6bq1avr1ltvTfRwUAxbt27VggULtGnTpvhj69atS+CISh8hO4F++eUX9e7dW7t27dJZZ52lu+66K9FDAsq9o1lOEGFnUyBpPPbYY3rmmWfkdDr16KOPMhmVomrXrq0lS5Zo2bJlevTRRxUIBDR27Fg988wziR5aqWG5iIk2bdqkp59+usDjxxxzTIEA/d133+muu+7SH3/8odNPP13Tp09nLWESKcq1RGrxer2SdNimFrHn2IsXSJxgMKgxY8Zozpw5crlcevzxx3XiiScmelgoJq/XG//398ILL1SdOnXUo0cP/etf/1KfPn3kcrkSPELzEbJN9Mcff+jtt98u8PhJJ510SDD76KOP1K9fP+Xm5qp79+6aNGmS4dpQJM7RXkuknrS0NHm9Xu3du1fBYFB2+6H/DAaDQe3du1cul0uVKlVK0CiBii07O1v333+/Pv/8c1WqVElPPfUUAbucOf7449WwYUP9/PPP+vXXX9WsWbNED8l0hGwTnXzyyUdcX/TGG29oxIgRCoVCuummmzRo0CB2L0hCR3MtkZosFouaNWum7777Tlu2bCnwD/vmzZsVDocN74gHUPr27dunm266SatXr1adOnX0zDPP8PuYgiKRiKZMmaJt27ZpypQpBSY0JMUnGIPBYFkPr0ywPqEMLVy4UMOHD1c4HNbgwYM1ePBgAjaQALH96hcuXFjgudhjXbp0KdMxAZD8fr9uv/12rV69Ws2aNdN///tfAnaKslgs+uijjzR//nzDhjO//vqrNm/eLK/XqyZNmiRghKWPkF1Gdu3apSFDhigcDqtv37666aabEj0koMK64oor5HK59Oyzz+qHH36IP/7999/rueeek9vt1vXXX5/AEQIV0/Tp0/Xtt9+qTp06mjVrFntip7hrrrlGkvTQQw9p+/bt8cd37Nihvn37KhgM6vrrry+X67EllouUmZkzZ2r//v1yOBxat26d+vfvb1h3/vnnswcoUMrq16+vQYMGacyYMerRo4dOOeUURSIRLV26VMFgUJMmTVK1atUSPUygQsnMzNSsWbMkRduojx8/vtDaqVOnltWwUAK9e/fW0qVL9emnn+rCCy9Uhw4dFAqFtGrVKuXk5KhLly66//77Ez3MUkPILiPLli2TJAUCAb3zzjuF1jVq1IiQDZSBnj17qm7dunruuef09ddfy+l0qkOHDrrrrrvUuXPnRA8PqHC+++475eXlSZJWr16t1atXF1pLyE4NDodDTz/9tF5++WW9+eabWr58uaxWq1q0aKErrrhC11xzTbneWc0SYUNYAAAAwFTl988HAAAAIEEI2QAAAIDJCNkAAACAyQjZAAAAgMkI2QAAAIDJCNkAAACAyQjZAAAAgMkI2QAAAIDJCNkAAACAyQjZAAAAgMkI2QAAAIDJCNkAAACAyQjZAAAAgMkI2QAAAIDJCNkAAACAyQjZAAAAgMkI2QAAAIDJ/h99Y0eZFoFouAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 251,
       "width": 364
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "plt.rc(\"font\", size = 18) #그림의 폰트 크기를 18로 고정\n",
    "gray = {\"facecolor\" : \"gray\"}\n",
    "black = {\"facecolor\" : \"black\"}\n",
    "red = {\"facecolor\" : \"red\"}\n",
    "green = {\"facecolor\" : \"green\"}\n",
    "blue = {\"facecolor\" : \"blue\"}\n",
    "\n",
    "a = np.array([1, 2])\n",
    "plt.plot(0,0,'kP', ms=20)\n",
    "plt.plot(a[0], a[1], 'ro', ms = 20)\n",
    "plt.annotate('', xy=[-0.6, 1.6], xytext=(0.2, 0.7), arrowprops=gray)\n",
    "plt.annotate('', xy=a, xytext = (0,0), arrowprops = black)\n",
    "plt.annotate('', xy=a + [-1, 1], xytext=(-1, 1), arrowprops = black)\n",
    "plt.text(0.35, 1.15, \"$a$\")\n",
    "plt.text(1.15, 2.25, \"$(1,2)$\")\n",
    "plt.text(-0.7, 2.1, \"$s$\")\n",
    "plt.text(-0.9, 0.6, \"평행이동\")\n",
    "plt.xticks(np.arange(-2, 4))\n",
    "plt.yticks(np.arange(-1, 4))\n",
    "plt.xlim(-2.4, 3.4)\n",
    "plt.ylim(-0.8, 3.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.23606797749979"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#벡터의 길이는 놈(norm)으로 정의\n",
    "\n",
    "a = np.array([1, 2])\n",
    "np.linalg.norm(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#스칼라와 벡터의 곱\n",
    "\n",
    "'''벡터에 양의 실수를 곱하면 방향은 변하지 않고 실수의 크기만큼 벡터의 길이가 커지고,\n",
    "음의 실수를 곱하면 벡터의 방향이 반대가 된다.'''\n",
    "\n",
    "a = np.array([1, 2])\n",
    "b = 2*a\n",
    "c=-a\n",
    "plt.annotate('', xy=b, xytext = (0,0), arrowprops = red)\n",
    "plt.text(0.8, 3.1, \"$2a$\")\n",
    "plt.text(2.2, 3.8, \"$(2,4)$\")\n",
    "plt.annotate('', xy=a, xytext=(0,0), arrowprops = gray)\n",
    "plt.text(0.1, 1.3, \"$a$\")\n",
    "plt.text(1.1, 1.4, \"$(1, 2)$\")\n",
    "plt.plot(c[0], c[1], 'ro', ms=10)\n",
    "plt.annotate('', xy=c, xytext = (0,0), arrowprops = blue)\n",
    "plt.text(-1.3, -0.8, \"$-a$\")\n",
    "plt.text(-3, -2.5, \"#(-1, -2)$\")\n",
    "plt.plot(0,0,'kP', ms=20)\n",
    "plt.xticks(np.arange(-5, 6))\n",
    "plt.yticks(np.arange(-5, 6))\n",
    "plt.xlim(-4.4, 5.4)\n",
    "plt.ylim(-3.2, 5.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 1.0, 0.9999999999999999)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#단위벡터\n",
    "\n",
    "a = np.array([1, 0])\n",
    "b = np.array([0, 1])\n",
    "c = np.array([1/np.sqrt(2), 1/np.sqrt(2)])\n",
    "np.linalg.norm(a), np.linalg.norm(b), np.linalg.norm(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#벡터의 합\n",
    "#방법 1 : 평행사변형\n",
    "\n",
    "a = np.array([1, 2])\n",
    "b = np.array([2, 1])\n",
    "c = a + b\n",
    "\n",
    "plt.annotate('', xy=a, xytext = (0,0), arrowprops = gray)\n",
    "plt.annotate('', xy=b, xytext = (0,0), arrowprops = gray)\n",
    "plt.annotate('', xy=c, xytext = (0,0), arrowprops = black)\n",
    "\n",
    "plt.plot(0,0,'kP', ms=10)\n",
    "plt.plot(a[0], a[1], 'ro', ms=10)\n",
    "plt.plot(b[0], b[1], 'ro', ms = 10)\n",
    "plt.plot(c[0], c[1], 'ro', ms = 10)\n",
    "\n",
    "plt.plot([a[0], c[0]], [a[1], c[1]], 'k--')\n",
    "plt.plot([b[0], c[0]], [b[1], c[1]], 'k--')\n",
    "\n",
    "plt.text(0.35, 1.15, \"$a$\")\n",
    "plt.text(1.15, 0.25, \"$b$\")\n",
    "plt.text(1.25, 1.45, \"$c$\")\n",
    "plt.xticks(np.arange(-2,5))\n",
    "plt.yticks(np.arange(-1, 4))\n",
    "plt.xlim(-1.4, 4.4)\n",
    "plt.ylim(-0.6, 3.8)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#방법 2 : 삼각형\n",
    "\n",
    "a = np.array([1, 2])\n",
    "b = np.array([2,1])\n",
    "c = a + b\n",
    "\n",
    "plt.annotate('', xy=a, xytext = (0,0), arrowprops = gray)\n",
    "plt.annotate('', xy=c, xytext = a, arrowprops = gray)\n",
    "plt.annotate('', xy=c, xytext = (0,0), arrowprops = gray)\n",
    "\n",
    "plt.plot(0,0, 'kP', ms = 10)\n",
    "plt.plot(a[0], a[1], 'ro', ms=10)\n",
    "plt.plot(c[0], c[1], 'ro', ms=10)\n",
    "\n",
    "plt.text(0.35, 1.15, \"$a$\")\n",
    "plt.text(1.45, 2.45, \"$b$\")\n",
    "plt.text(1.25, 1.45, \"$c$\")\n",
    "\n",
    "plt.xticks(np.arange(-2, 5))\n",
    "plt.yticks(np.arange(-1, 4))\n",
    "plt.xlim(-1.4, 4.4)\n",
    "plt.ylim(-0.6, 3.8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#둘 중 하나를 평행이동해도 벡터의 합의 결과는 마찬가지.\n",
    "#벡터의 합은 교환법칙이 성립한다.\n",
    "\n",
    "a = np.array([1, 2])\n",
    "b = np.array([2, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a + b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = b + a\n",
    "c"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}