Given a 3-D point at position (20, 35, 10), determine the coordinates of the point that results from rotating the original point 90 degrees around the axis defined by the vector (1, 1, 1). Use the formula:
P2 = Rx-1(α) Ry-1(β) R2(θ) Ry(β) Rx(α) P1
Show each of the intermediate matrices. Refer to section 9-1 of the textbook for the details of how matrices are calculated. Because no translations are involved, you can use 3 x 3 matrix math for your calculations.