So here's the problem:

"Let A = (0,0,0), B = (2,0,0), C = (1, sqrt(3), 0), and D = (1, 1/sqrt(3), 2*sqrt(2/3).

a) Show that A, B, C, D are all the same distance from each other.

b) Find the point P = (x, y, z) which is equivalent from A, B, C, and D by setting up and solving three equations in x, y, and z."

I'm not sure how to go about solving this problem. For a, can I simply find the length of each vector and compare them?

And for b, I honestly have no idea. Help?