Reference no: EM131614132

Question: Let A = (0, 0, 0), B = (2, 0, 0), C = (1, √3, 0) and D = (1, 1/√3 , 2, √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) that is equidistant from A, B, C and D by setting up and solving three equations in x, y, and z.

(c) Use the dot product to find the angle AP B. (In chemistry, this angle is often approximated by 109.5°. A methane molecule can be represented by four hydrogen atoms at points A, B, C and D, and a carbon atom at P.)