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   "source": [
    "# Chapter 01: Vectors and their use"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.1:pg-25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Resultant R= 40.31  cm\n",
      "\n",
      "Theta= 120.0  degrees\n"
     ]
    }
   ],
   "source": [
    "  #Example 1_1\n",
    "import math  \n",
    "  #To add the given Displacements Graphically\n",
    "d1=25     #units in cm\n",
    "d2=10     #units in cm\n",
    "d3=30     #units in cm\n",
    "R=math.sqrt(d1**2+d2**2+d3**2)    #units in cm\n",
    "theta1=30     #units in degrees\n",
    "theta2=90    #units in degrees\n",
    "theta3=120    #units in degrees\n",
    "theta=360-(theta1+theta2+theta3)    #units in degrees\n",
    "print \"The Resultant R=\",round(R,2),\" cm\\n\"\n",
    "print \"Theta=\",round(theta),\" degrees\"\n",
    "  #In text book the answer is printed wrong as R=49cm and theta=82 degrees but the correct answer is R=40.31cm and theta=120 degrees\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.2:pg-25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Resultant R= 6.72  Meters\n",
      "\n",
      "The Angle theta= 170.0  degrees\n"
     ]
    }
   ],
   "source": [
    "  #Example 1_2\n",
    "\n",
    "import math\n",
    "  \n",
    "  # To add the given vector displacements\n",
    "a=1    #units in meters\n",
    "b=3    #units in meters\n",
    "c=5    #units in meters\n",
    "d=6    #units in meters\n",
    "theta1=90    #units in degrees\n",
    "Rx_a=a*math.sin(theta1*math.pi/180)     #units in meters\n",
    "Rx_b=round(b*math.cos(theta1*math.pi/180))   #units in meters\n",
    "theta2=37     #units in degrees\n",
    "Rx_c=-round(c*math.cos(theta2*math.pi/180))       #units in meters\n",
    "theta3=53    #units in degrees\n",
    "Rx_d=-d*math.cos(theta3*math.pi/180)\n",
    "Ry_a=round(a*math.cos(theta1*math.pi/180))     #units in meters\n",
    "Ry_b=round(c*math.sin(theta2*math.pi/180))   #units in meters\n",
    "Ry_c=round(c*math.sin(theta2*math.pi/180))   #units in meters\n",
    "Ry_d=-(d*math.sin(theta3*math.pi/180))   #units in meters\n",
    "Rx=Rx_a+Rx_b+Rx_c+Rx_d       #units in meters\n",
    "Ry=Ry_a+Ry_b+Ry_c+Ry_d       #units in meters\n",
    "R=sqrt(Rx**2+Ry**2)    #units in meters\n",
    "phi=round(math.atan(Ry/-(Rx))*180/math.pi)      #units in degrees\n",
    "phi=180-phi     #units in degrees\n",
    "print \"The Resultant R=\",round(R,2),\" Meters\\n\"\n",
    "print \"The Angle theta=\",round(phi),\" degrees\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.3:pg-26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultant R= 15.5  Meters\n",
      "\n",
      "Angle Theta= 19.0  Degrees\n"
     ]
    }
   ],
   "source": [
    "  #Example 1_3\n",
    "\n",
    "import math\n",
    "  #To subtract vector B from Vector A\n",
    "Ax=8.7    #units in meters\n",
    "Ay=5     #units in meters\n",
    "Bx=-6     #units in meters\n",
    "By=0     #units in meters\n",
    "Rx=Ax-Bx       #units in meters\n",
    "Ry=Ay-By        #units in meters\n",
    "R=sqrt(Rx**2+Ry**2)      #units in meters\n",
    "theta=round(math.atan(Ry/(Rx))*180/math.pi)      #units in degrees\n",
    "print \"Resultant R=\",round(R,1),\" Meters\\n\"\n",
    "print \"Angle Theta=\",round(theta),\" Degrees\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex1.4:pg-30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volume V= 5.65e-10 Meter**3\n"
     ]
    }
   ],
   "source": [
    "  #Example 1_4\n",
    "import math\n",
    "\n",
    "  #To calculate the Volume\n",
    "r=3*10**-5    #units in meters\n",
    "L=0.20    #units in meters\n",
    "V=math.pi*r**2*L    #Units in meter**3\n",
    "print \"Volume V=\",round(V,12),\"Meter**3\"\n"
   ]
  }
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