The equation of plane:
$ Ax + By + Cz = d$
Where $ A \hat i + B \hat j + C \hat k$ is the normal vector $ \vec n$ perpendicular to the plane.
The position vector $ \vec r = x \hat i + y \hat j + z \hat k$
$ \vec r \cdot \vec n = d$
This last equation says that a position vector to any point on the plane has the same projection along $ \vec n$ because $d$ is a constant.
But I can't see that graphically. Different position vectors to the plane have different slopes, while the normal vector of the plane is always perpendicular and doesn't change, so how does every position vector to any point on the plane have the same projection along $ \vec n$? Thank you.