a) ( . ) T= [1 2 3]" represents a translation in 3D space. Find the corresponding 4-by-4 homogeneous transformation HT, that will represent the same transformation in homogeneous coordinates. b) ( 15) 3-by-3 matrix R represents the rotation matrix that rotates the points ti/4 radians around z-axis in the counter- clockwise direction in 3D space using the right hand convention. Find R matrix. Find the corresponding 4-by-4 homogeneous transformation HR, that will represent the same transformation in homogeneous coordinates. C) Find the transformation defined by HTHR. d) 1 Find the transformation defined by HRHT