(a) Given a general (not necessarily rectangular) tetrahedron, let denote vectors whose lengths are equal to the areas of the four faces, and whose directions are perpendicular to the these faces and point outward. Show that .
(b) Now consider a rectangular tetrahedron, i.e., one which has one vertex at which all three angles are right angles. Let D denote the area of the face opposite this rectangular vertex (i.e., the analog of a hypothenuse), and let A;B;C denote the areas of the other three faces. Prove that .