Consider a plane given by the equation
Find the Cartesian equation for a plane parallel to this one and the same distance as this plane from the point .
Since the requested plane is parallel to the given plane we know that they must have the same normal vector, . Therefore, the Cartesian equation of the requested plane is of the form
From the previous exercise (Section 13.17, Exercise #19) we know the distance from to a plane is given by the formula
Therefore, the distance from the given plane to the point is
Since the distance from the point to the requested plane must be the same we must have
(Since the solution belongs to the other plane.)