Thanks for your reply - it helped me out of my blockade.
I was too fixed at the implicit characterisation of orthogonal points to P by the equation
P' ( x - P ) = 0.
You are right, exept a typo in the sign for z in your formula.
Points or vectors, that is an old discussion. "Vectors" are...
I have a given point (vector) P in R^3 and a 2-dimensional linear subspace S (a plane) which consists of all elements of R^3 orthogonal to P.
The point P itself is element of S.
So I can write
P' ( x - P ) = 0
to characterize all such points x in R^3 orthogonal to P. P' means the transpose...