Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
  A unit vector in any direction has a magnitude (length) 1. The unit vectors parallel to the cartesian $x, y$ and $z$ coordinates are usually designated by $\hat\imath, \hat\jmath$ and $\hat k$ respectively. In terms of these unit vectors, the vector $\vec A$ is written
 
\begin{displaymath}\vec A = \hat\imath A_x + \hat\jmath A_y + \hat k A_z\end{displaymath}
  Any vector in 3 dimension may be written in this fashion. The vectors $\hat\imath, \hat\jmath, \hat k$ are said to form a basis . In fact, any three non-colinear vectors may be used as a basis. The basis vectors used here are perpendicular to one another. A unit vector along the direction of $\vec A$ is
 
\begin{displaymath}\hat A = \frac{\vec A}{\mid A\mid}\end{displaymath}
   
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