Derivation of Plane Equation

To derive equation of the plane given three points: P1, P2, P3
[ P2 - P1] x [ P3 - P1] = N, orthogonal vector

Given a general point P = (x,y,z)
N * [P - P1] = 0 if P is in the plane.

Or given a point (x,y,z) in the plane and normal vector N then N*[x,y,z] = -D