Converting arbitrary Cartesian vector to cylindrical

[playoff]

Hello PF, I have a problem to solve in the following form: Given a vector with Cartesian components, V={Vx,Vy,Vz}, find its components in circular cylindrical coordinate.

Given the actual vector components, it'd be very easy to convert. But I have no idea where to start on this. Any guide to where to start from will be much appreciated!

 

[jedishrfu]

If the z component were zero then what kind conversion would it be?

 

[playoff]

Well, its a cylindrical coordinate, so Vz wouldn't go over any transformation, right? So if Vz=0, then after the conversion it will still be 0. I am still very lost...

 

[jedishrfu]

I was hoping you'd recognize it as a conversion from x,y to polar coordinates. Cylindrical are an extension of polar to 3D by adding the z component.