Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  Spherical Polar Coordinates :
 

Spherical coordinates are useful in dealing with problems which possess spherical symmetry. The independent variables of the system are $(r,\theta, \phi)$. Here $r$ is the distance of the point $P$ from the origin. Angles $\theta$ and $\phi$ are similar to latitudes and longitudes.
Two mutually perpendicular lines are chosen, taken to coincide with the x-axis and z-axis of the cartesian system. We take angle $\theta$ to be the angle made by the radius vector (i.e. the vector connecting the origin to P) with the z-axis (the angle $\theta$ is actually complementary to the latitude). The angle $\phi$ is the angle between the x-axis and the line joining the origin to $P^\prime$, the foot of the perpendicular from $P$ to the x-y plane.
The unit vectors $\hat r, \hat\theta$ and $\hat\phi$ are respectively along the directions of increasing $r, \theta$ and $\phi$.

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