Derivation of point-to-plane distance from Vector edition

Plane equation: p*n + d = 0, p is a point on the plane, N is normal, and D is the distance from the origin to the plane.

The derivation of the point-to-plane distance, with the emphasis on normal n being the unit vector, simplifies the derivation and makes it easier to understand.

:

First: Q to plane distance r = | Q-q ' |

Second: Plane normal vector N and q-q ' parallel, and because N is a unit vector, can get q-q ' = rn

Then: q = rn + Q ', then multiply the two sides by n NQ = rn*n + q ' n

After: Because Q ' is on the plane, so the plane equation is Q ' n + d = 0, i.e. Q ' n =-D

Finally: n is the unit vector, with NQ = R + (-D), i.e. R = NQ + D

Derivation of point-to-plane distance from Vector edition