I'm interested in finding the general form of the equation of a plane, using Cartesian coordinates. I know the answer to this is that any given plane is described by the equation $ax+by+cz+d=0$.
However, most derivations of the above equation employ the use of a vector perpendicular to the given plane. Is there a derivation which depends only on knowledge of Euclidean and analytic geometry, without using vectors? If yes, I would really appreciate seeing such a derivation.