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+{
+"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)"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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