Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  Cylindrical coordinates :
  Cylnidrical coordinate system is obtained by extending the polar coordinates by adding a z-axis along the height of a right circular cylinder. The z-axis of the coordinate system is same as that in a cartesian system.
  In the figure $\rho$ is the distance of the foot of the perpendicular drawn from the point to the $ x-y (\rho,\theta)$ plane. Note that $\rho$ here is not the distance of the point P from the origin, as is the case in polar coordinate systems. (Some texts use $r$ to denote what we are calling as $\rho$ here. However, we use $\rho$ to denote the distance from the origin to the foot of the perpendicular to avoid confusion.) In terms of cartesian coordinates
 
\begin{eqnarray*} x&=& \rho\cos\theta\\ y&=& \rho\sin\theta\\ z&=&z \end{eqnarray*}
  so that the inverse relationships are
 
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