Question: Please show the steps in solving this problem. (a) Consider the following sequence of rotations. The frame first rotates by 30 about the current y-axis,

Please show the steps in solving this problem.

(a) Consider the following sequence of rotations. The frame first rotates by 30" about the current y-axis, and then it rotates by 45 about the current x-axis. Write the matrices R. , Ry,y and the product that gives the resulting rotation matrix symbolically and numerically. (b) A targeted object is displaced at 6 units in the xo-direction. Find the corresponding homogeneous vector d. (c) Find the homogeneous transformation matrix H based on (a) and (b). (d) If a sensor is located at p = [4 0 3.2] , find the position measured from frame 0, or p . (e) Synthesize the inverse of the homogeneous transformation matrix H-1. (f) Prove that the procedures can reverse transformation and lead to p. (Detail derivation is required for the credit. Single equation in this part will get 0 point.)

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