Let [math]u = OA, v = OB, w = OC[/math] and P in the green triangle [math](1,0,0), (0,1,0), (0,0,1)[/math] [br][math]PP = x(P)*u + y(P)*v + z(P)*w [/math]. The red triangle ABC is the image of green triangle.[br][br][url]http://math.stackexchange.com/questions/961912/vector-linear-combinations-in-3d-space[/url]