vector projection based on adopted direction

I have X'Y'Z' coordinate system (define by position of X', Y', Z' axises). This coordinate

system was created by rotatation and tilting "the matlab coordinate system" (XYZ).

I have also point (vector) P which I would like to project onto X'Y' plane. This projection I would like to

do orhogonaly in X'Y,Z' coordinate system (projection direction parallel to Z' axis) - results: PF.

So far I create plane X'Y' and do "simple" orthogonal projection, but in this case I project

point P parallel to Z axis and get PP result.

If there's any way to make a projection using Z' direction?

[darova]

Any ideas?