Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
Elementary Vector Algebra :
  Geometrically a vector is represented by a directed line segment. Since a vector remains unchanged if it is shifted parallel to itself, it does not have any position information.
  A three dimensional vector can be specified by an ordered set of three numbers, called its components . The magnitude of the components depend on the coordinate system used. In electromagnetism we usually use cartesian, spherical or cylindrical coordinate systems. (Specifying a vector by its components has the advantage that one can extend easily to n dimensions. For our purpose, however, 3 dimension would suffice.)
  A vector $\vec A$ is represented by $(A_x, A_y, A_z)$ in cartesian (rectangular) coordinates. The magnitude of the vector is given by
 
\begin{displaymath}\mid A\mid = \sqrt{A_x^2+A_y^2+A_z^2}\end{displaymath}
 
\includegraphics{fig1.1.eps}
 
 
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