Without using vectors, I placed one of the faces (an equilateral triangle) as the base. The top vertex is right above the center of that face. The center of the face is from the center, and the top vertex is from the center. Using Pyth. Theorem,
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
then
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.
Thanks for your help, I guess that's a lo easier than what I was trying to do. But unfortunately I have to do the question using vectors (point of the whole exercise...)
I know I need to do the dot product of the position vector of the centre of face with something else, but I don't know what else, so any pointers please?