{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 3: Vectors"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.1: Sample_Problem_1.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci', -1)\n",
"\n",
"//Given that\n",
"a = [2,0]\n",
"b = [2 *cos(dtor(30)),2 *sin(dtor(30))]\n",
"c = [-1,0]\n",
"\n",
"//Sample Problem 3-1\n",
"printf('**Sample Problem 3-1**\n')\n",
"poss = [norm(a+b+c) norm(a-b+c), norm(a+b-c), norm(a-b-c)]\n",
"max_norm = 0\n",
"for v = poss\n",
"    if v > max_norm  then max_norm = v        \n",
"    end\n",
"end\n",
"printf('The maximum possible value is %f m', max_norm)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.2: Sample_Problem_2.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci', -1)\n",
"\n",
"//Given that\n",
"dis = 215  //in km\n",
"position = [dis * cos(dtor(22)), dis * sin(dtor(22))]\n",
"\n",
"//Sample Problem 3-2\n",
"printf('**Sample Problem 3-2**\n')\n",
"printf('The plane is %f km in the north & %f in the east', position(1),position(2))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.3: Sample_Problem_3.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"\n",
"//Given that\n",
"displacement_vector = [-2.6,-3.9,.025]    //each in km\n",
"\n",
"//Sample Problem 3-3\n",
"printf('**Sample Problem 3-3**\n')\n",
"mag = norm(displacement_vector)\n",
"sw_angle = atan(displacement_vector(2)/displacement_vector(1))\n",
"up_angle = displacement_vector(3)/norm(displacement_vector)\n",
"printf('The team displacement vector had a magnitude %f km,\n and was at an angle of %d south of west and\n at an angle of %f upward', mag, rtod(sw_angle), rtod(up_angle))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.4: Sample_Problem_4.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"\n",
"//Given that\n",
"a = [4.2,-1.5]\n",
"b = [-1.6,2.9]\n",
"c = [0,-3.7]\n",
"\n",
"//Sample Problem 3-4\n",
"printf('**Sample Problem 3-4**\n')\n",
"r = a + b + c\n",
"magnitude = norm(r)\n",
"angle = rtod(atan(r(2)/r(1)))\n",
"printf('The magnitude of the vector is %f m & the angle measured from the x axis is %f', magnitude, (angle) )"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.5: Sample_Problem_5.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"\n",
"//Given that\n",
"a = [36,0]   //in km\n",
"c = [25 *cos(dtor(135)), 25 *sin(dtor(135))]   //in km\n",
"d_mag = 62  //in km\n",
"\n",
"//Sample Problem 3-5\n",
"printf('**Sample Problem 3-5**\n')\n",
"//we have a + b + c = d\n",
"//therefore ax = bx + cx + dx\n",
"// bx = 0\n",
"d_x = a(1) + c(1)\n",
"d_y = d_mag * sqrt(1 - (d_x/d_mag)^2)\n",
"d = [d_x, d_y]\n",
"b = d(2) - a(2) - c(2)\n",
"printf('The magnitude of b is equal to %f km', b)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.6: Sample_Problem_6.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"\n",
"//Given that\n",
"a = [3,-4,0]\n",
"b = [-2,0,3]\n",
"\n",
"//Sample Problem 3-6\n",
"printf('**Sample Problem 3-6**\n')\n",
"angle_ab = acos(-norm(a*b')/(norm(a) * norm(b)))\n",
"printf('The angle between given vectors is %f degress', rtod(angle_ab))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.7: Sample_Problem_7.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"exec('cross_product.sci',-1)\n",
"\n",
"//Given that\n",
"a = [18 * cos(dtor(250)), 18 * sin(dtor(250)),0]\n",
"b = [0,0,12]\n",
"\n",
"//Sample Problem 3-7\n",
"printf('**Sample Problem 3-7**\n')\n",
"cross_ab = crossproduct(a,b)\n",
"angle_x = acos(cross_ab(1)/norm(cross_ab))\n",
"printf('The magnitude of cross product of given vectors is %f \n and angle  with the x axis in degrees is %f', norm(cross_ab),rtod(angle_x))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.8: Sample_Problem_8.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('degree_rad.sci',-1)\n",
"exec('cross_product.sci',-1)\n",
"\n",
"//Given that\n",
"a = [3,-4,0]\n",
"b = [-2,0,3]\n",
"\n",
"//Sample Problem 3-8\n",
"printf('**Sample Problem 3-8**\n')\n",
"cross_ab = crossproduct(a,b)\n",
"printf('The cross product of given vectors is ')\n",
"disp(cross_ab)"
   ]
   }
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		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
			}
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