How do you find the distance between two 3D planes?
First note that for the distance between two planes in 3 dimensions to be nonzero they must never intersect. But two planes in 3D never intersect iff
(1) they are parallel and
(2) they are not coincident (not coincident means they’re not just two names for the same plane).
Two parallel planes have the same normal vector. So what you need to do is take any point P on your first plane and any point Q on your second plane and construct the vector PQ→. Then the projection of this vector onto a normal vector to the planes will be a vector from the first plane to the second in the direction perpendicular to the planes. Hence its length will be the distance between the planes.