1. Derive the 4x4 Rotation and Translation matrix about the Y axis at angle 8.Show your work at each step.Answers without details will not be accepted. a. Sketch the vector orientation for a ccw rotation about the Ry(theta) axis. Show each unit vector and associated rotation components. Assume is the angle between the rotated vector and the Rx(kyi) axis.b. Derive the unit vector equations relating the unit vectors in the local frame[i k]to the fixed frame [i k]^t.

c.From the above, determine the 2D rotation matrix A, [Rx Rz]™= A[Rx Rz]¹,where A is the rotation matrix and [Rx R₂]^t are the coordinates in the local frame.

d. From the above determine the spatial (3D) rotation matrix A, where [ Rx Ry Rz]™= A[ Rx RyR₂]^t, about the Y axis.

e. Given the coordinates of the origin of the Local Frame with respect to the Fixed Frame as[rxl ryl rzl]^t, from part (d), determine the 4D rotation and translation matrix,AR, about the Y axis.