A cube has vertices at the eight points (x, y, z) where each ofx, y, and z are either −1 or 1.

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

(b) Find the gneneral equation of the plane that contains thediagonal from (−1, −1, −1) to (1, 1, 1) and is perpendicular to thexy-plane.

(c) Determine the angle of the diagonals of two adjacent facesof the cube.