Let be a point in a plane, and be a normal vector to the plane. Then the plane is described by the following equation

.

Example 2

A plane is given the equation

.

Find a unit normal vector u to the plane and any two points in the plane.

Solution: Since n = {1, -2, 3} and ,

.

Setting x = y = 0, we obtain z = 2.

Likewise, if x = z = 0 then from the equation of the plane follows y = -3.

Therefore, and are points in the given plane.