(A,B,C) is the normal vector for plane Ax+By+Cz+D=0. why?

for any point (x,y,z) and a fixed point (x0, y0, z0) on a plane,

(x-x0, y-y0, z-z0) is a vector lying on the plane and its dot product with

normal vector (a, b, c) should be zero.

a(x-x0) + b(y-y0) + c(z-z0) = 0

Since this much be true for ANY x, y, z on the plane, it implies a=A, b=B and c=C