Problem 1. (28 pts) Suppose OT, = Trans([ 1 1/2 ]")Rot(7/6) and 'T, = Trans([ 3/4 3/4 ]")Rot(--/4): (a) (7 pts) Draw a diagram to scale showing the relative locations of frames 0, 1, and 2. (b) (7 pts) Suppose point P is fixed and it is located by P2 = P-02. Suppose ?p2 draw P2 in your diagram. Find 'P2 and "p2 (i.e., the same vector in different frames). (e) (7 pts) Suppose pi = P - 01: draw pi in your diagram. Use ?p2 and 'T, (i.e., create it based on the given information), and find 'P. (i.e., use homogeneous transformation). (d) (7 pts) Suppose po = P - 0o; draw po in your diagram. Use ?p2 and "T, (i.e., create it based on the given information), and find p. (i.e., use homogeneous transformation). -[1] Problem 1. (28 pts) Suppose OT, = Trans([ 1 1/2 ]")Rot(7/6) and 'T, = Trans([ 3/4 3/4 ]")Rot(--/4): (a) (7 pts) Draw a diagram to scale showing the relative locations of frames 0, 1, and 2. (b) (7 pts) Suppose point P is fixed and it is located by P2 = P-02. Suppose ?p2 draw P2 in your diagram. Find 'P2 and "p2 (i.e., the same vector in different frames). (e) (7 pts) Suppose pi = P - 01: draw pi in your diagram. Use ?p2 and 'T, (i.e., create it based on the given information), and find 'P. (i.e., use homogeneous transformation). (d) (7 pts) Suppose po = P - 0o; draw po in your diagram. Use ?p2 and "T, (i.e., create it based on the given information), and find p. (i.e., use homogeneous transformation). -[1]