Cross Product in Spherical Coordinates
There is no simple formula for the cross product of vectors expressed in spherical polar coordinates. It is, however, possible to do the computations with Cartesian components and then convert the result back to spherical coordinates. This Demonstration enables you to input the vectors and then read out their product , all expressed in spherical coordinates. The vectors are displayed at the bottom of the graphic, with the angles expressed as multiples of .
Snapshot 1: Setting and are in the , plane and has only a -component.
Snapshot 2: This shows the Cartesian unit vector relationship .
Snapshot 3: The vector product of two collinear vectors equals zero.