- Prove that the distance from the point to the plane
is given by the formula
- Find the point on the plane which is nearest to the point .
- Proof. By Theorem 13.6 (page 476 of Apostol) we know that the distance from a point to a plane is given by
- A normal to the plane is given by . So, for any point . Further, the distance from to a point not on is minimal when where
Naming to be the point we have