Vector Cross Product Formula in Spherical & Cylindrical Coordinates

[astrosona]

Hello all,

it might be funny! but i am stuck to it! what is the vector cross product formula in spherical and cylindrical coordinates?!

I know for Cartesian coordinate we have that nice looking determinant. but what about the other coordinates. I had looks to all the math books (like Botckov, Arfken ,...) that i knew but i couldn't find it. all i had found was for curl of vectors in different coordinates.


I appreciate your help in advance,
sona

 

[pam]

The same type of determinant works with r, theta, phi unit vectors.

 

[HallsofIvy]

Check this
http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
for the appropriate unit vectors.