is a vector normal to the plane containing and and whose magnitude is equal to the area of the parallelogram defined by them, and so twice the area of the triangle defined by them.

Now the absolute value of is equal to the product of the projection of onto , which is the height of the tetrahedron times twice the area of the base (upto the sign).

Thus , is equal to the height of the tetrahedron times twice the area of the base, which is six times the volume of the tetrahedron, which is what was to be proven.

RonL