I'm not quite sure what I'm being asked to prove here. I presumably have to show that P satisfies some equation that shows it is a plane and not some other kind of surface but I don't know what that equation is.
If you use a vector formalism, the equation of the plane is same in 3 or 4 or other dimension.
Let n is a normal, so it is perpendicular to the plane, therefore their inner product (or scalar product) is null. So the equation is: