Thread Subject: Mapping a vector onto a surface

Ok, this may be more of a maths question.

I have a three dimensional surface Z, which exists in x, y and z.

I also have a vector, which is in the x-y plane. I want to map this vector onto the surface. Any ideas?

Also, once i've mapped the vector onto surface Z I then want to be able to see what the projecion of this new vector would be on the x-z plane.

Any help would be appreciated. I'm totally stuck!!

Thanks