A cube has vertices at the eight points (x, y, z), where each of x, y, and z is either 0...

A cube has vertices at the eight points (x, y, z), where each of x, y, and z is either 0 or 1. (See Figure 1.34.)

(a) Find the general equations of the planes that determine the six faces (sides) of the cube.

(b) Find the general equation of the plane that contains the diagonal from the origin to (1, 1, 1) and is perpendicular to the xy-plane.

(c) Find the general equation of the plane that contains the side diagonals referred to in Example 1.22.