Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
Scalar Product (The Dot products)
  The dot product of two vectors $\vec A$ and $\vec B$ is a scalar given by the product of the magnitudes of the vectors times the cosine of the angle ( $\le 0\le\theta$) between the two
 
\begin{displaymath}\vec A\cdot\vec B = \mid A\mid \mid B\mid\cos\theta\end{displaymath}
  In terms of the components of the vectors
 
\begin{displaymath}\vec A\cdot\vec B = A_xB_x+A_yB_y+A_zB_z\end{displaymath}
  Note that
Dot product is commutative and distributive
 
\begin{eqnarray*} \vec A\cdot\vec B &=&\vec B\cdot\vec A\\ \vec A\cdot(\vec B+\vec C) &=&\vec A\cdot\vec B +\vec A\cdot\vec C \end{eqnarray*}
   
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