I'm stuck on this question:
Q: The vectors a, b, and c are of equal length l, and define the positions of the points A, B, and C relative to O. If OABC is a regular tetrahedron, find the distance of one vertex from the opposite face.
My attempt at the question was as follows:
Let the vector normal to the plane ABC be
distance d is the projection of c onto a, so
but if I substitute equation 1 into 2 it gives rise to a very complicated equation and I know I need to use the fact that a, b, and c are of length l.
Any help and pointers would be much appreciated.