22 Use determinants to calculate volume

• In 2D the triangular area of two points P & Q and the origin is:

        A = 0.5   | Px Py |
                  | Qx Qy |
  

• In 3D the (oriented) volume of a tetrahedron formed by three points P, Q, & R and the origin is:

                P . Q x R     1  | Px Py Pz |
        V =     ---------  =  -  | Qx Qy Qz | 
                    6         6  | Rx Ry Rz |