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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