Module 1 : A Crash Course in Vectors
Lecture 1 : Scalar And Vector Fields
Position Vector and its Transformation under Rotation
  Though a general vector is independent of the choice of origin from which the vector is drawn, one defines a vector representing the position of a particle by drawing a vector from the chosen origin O to the position of the particle. Such a vector is called the position vector . As the particle moves, the position vector also changes in magnitude or direction or both in magnitude and direction. Note, however, though the position vector itself depends on the choice of origin, the displacement of the particle is a vector which does not depend on the choice of origin.
  In terms of cartesian coordinates of the point , the position vector is
 
\begin{displaymath}\vec r = \hat\imath x + \hat\jmath y + \hat k z\end{displaymath}
  We will now derive the relationship between the $x,y,z$ and the corresponding values $x^\prime, y^\prime, z^\prime$ in a coordinate system which is rotated with respect to the earlier coordinate system about an axis passing through the origin. For simplicity consider the axis of rotation to be the z-axis so that the $z$ coordinate does not change.
 
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