Construct an example of a parallelepiped in 3-space, providing the coordinates of all vertices (refer to the figure below).
In the example of the constructed parallelepiped, show that U1 Uz U3 IAA (AD x AB) - Idet V1 Vz V3 LW1 Wz W3
where AA' (u1, uz, U3), AD = (V1, Vz, V3), AB = (W1, Wz, W3).