Here is the distance formula for points in 3D. That should solve part A for you.
Use that same formula for part B. In terms of x,y, and z set up a system of equations using the distance formula, with respect to points A,B,C, and D.
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?