Given a point p = (3, 1, 2) and using the homogenous representation:

(a) calculate the coordinates of the transformed point p* if p is rotated about the x, y, and z axes by angles 60°, 30°, and 60° respectively.
(b) if the point p* obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. verify your answer.
(c) calculate p* if p is translated by d = 2i – 3j + k and then scaled uniformly by s=3.0.