Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
Scalar Multiplication
  The effect of multiplyimg a vector by a real number $c$ is to multiply its magnitude by $c$ without a change in direction (except where $c$ is negative, in which case the vector gets inverted). In the component representation, each component gets multiplied by the scalar
 
\begin{displaymath}c\vec A = (cA_x, cA_y, cA_z)\end{displaymath}
  Scalar multiplication is distributive in addition, i.e.
 
\begin{displaymath}c(\vec A + \vec B) = c\vec A + c\vec B\end{displaymath}
  Two vectors may be multiplied to give either a scalar or a vector.
   
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