A non-zero vector is a normal vector to the plane if N is perpendicular to both A and B.
Consider a plane in R3. Let . Then
(a) N is a normal vector to M.
(a) Follows from properties (d) and (e) of Theorem 2.12.
(b) Proof is analogous to that for the line discussed in section 2.5.
Given a plane M through P with a normal vector N and
Then, , where the equal sign applies iff
Proof is analogous to that for the line discussed in Theorem 2.6.
The shortest distance from a point Q to a plane M is
Actually, d is called the distance from Q to M.