Question

Find an equation of the plane that passes through the point P0 = (6, 3, 2) and is parallel to the xy-plane. g

Answer 1

The xy-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.

Then the equation of the plane through (6, 3, 2) that is parallel to the xy-plane has equation

〈x - 6, y - 3, z - 2〉 • 〈0, 0, 1〉 = 0

==>   z - 2 = 0

==>   z = 2