Problem 5 Find the rotation matrix that will line up the orthogonal vectors, 1 1 A: 1 and B: 2 , 1 1 along the y and zaxes, respectively. 1. (10 points] VAM Problem 5 [see page 30) asks you to rotate a vector into the y-axis and another vector into the z-axis. The questions below will help you to rotate A into the yaxis. For this problem submit your work for rotating both A and B as asked in the assignment problem. '12) rotate A into the y-axis you have to apply successive rotations to zero out the :1: and z components. Follow these steps: (a) Draw a picture that shows the vector projected into the icy-plane. (This projected vector has 9: and 3; components that are both 1 unit of length.) (b) To rotate the projected vector about the zaicis, mark the angle between the y-axis and the projected vector A. Using the picture, determine the sine and cosine of the angle you. marked. The rotation matrices use the sine and cosine of this angle so you may not actually need to know the value of the angle. {Read questions carefully!) (c) Generate the rotation matrix [call it R1) for a rotation about the z-axis and apply it to the vector A: Determine A' = RlA. If you did this correctly, the r-component will be 0 at the end. Take care to note this is a coimterclockwise (positive) rotation. (d) The nal steps now require a rotation about the r-axis to zero out the y-component. As above, draw a picture with the new 3; and 2: components. Mark the angle be- tween the rotated vector and the y-axis. Use the picture to determine the sine and cosine of the angle. Write the rotation matrix (for a rotation about the r-axis; call it R2). Apply the rotation matrix to the rotated vector: A\" = RZA". If you did this correctly, you will get A" = y. Note that this step requires a clockwise (negative) rotation. (e) The total rotation matrix for this process is R = R2 R1