Prove that if (c-a).b=0 and (c-b).a=0 and (b-a).c=0. SHow that this can be used to prove the following geometrical results.
a) The lines through the vertices of the triangle ABC perpendicular to the opposite sides meet in a point.
b) If the tetrahedron AOBC has two pairs of perpendicular opposite edges, the third pair of edges is perpendicular.
Prove also that , in both cases OA2+BC2=OB2+CA2=OC2+AB2
Please help...