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  3. consider the following sequence of rotations...

Question: consider the following sequence of rotations...

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Consider the following sequence of rotations:

I. Rotate by ф about the current y-axis. 2, Rotate by ψ about the current x-axis. (a) If the angles are φ = 30° and ψ= 45°, write the matrix product that will give the resulting rotation matrix. You need to include three matrices: Ry.φ, Rx , and the corresponding transformation matrix (b) If the targeted object also has a displacement of 4 units in the xo-direction, find the corresponding homogeneous vector d and the homogeneous transformation matrix H (c) If a sensor is located at pl = [3.2 0 1.2]T, find the position measured from fame o, orp. (d) Synthesize the inverse of the homogeneous transformation matrix H-1 and show the procedures that the reverse transformation can lead to p.

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