Today I had my first classical mechanics class (upper level undergraduate studies; I'm so glad!) and I'm already stuck with some "basic" math. I am however willing to put all my effort in solving all the problems.

I have to convert the versors , and into the versors of cylindrical and spherical coordinates, namely , , for cylindrical coordinates and , and for spherical coordinates.

I've tried to write as a linear (or non linear?) combination of and in cylindrical coordinates. But I always end up with . Some of the students that could solve the problem ended up with . I'm totally clueless about how to reach the good result. How can I start?

I'm also asked to convert cylindrical versors into spherical ones and all other possible conversions.

I just need a push up in the right direction, I'm going to do all the arithmetic and everything involved in solving the problem, but I need a start-point.

Thank you very much in advance.