Please answer both a) and b) and show your work

The following question regarding computer graphics in OpenGL:

Thank you!

(1) (6 marks) We have discussed in class that a rotation around an arbitrary axis can be decomposed into a series of transformations. Look at the following picture that has been discussed in class and whose purpose is to show that we try to rotate the arbitrary axis such that it aligns with the positive direction of the z-axis. Olx ay al Z In the picture, the unit vector whose head is at (Qx, dy, az) is the axis about which the rotation is to be conducted. O, is the angle we rotate the unit vector, about the direction of the x-axis, such that it eventually lies in the xz plane. Then the unit vector is rotated Oy degrees about the direction of the y-axis such that it aligns with the positive direction of the z-axis. (a) (2 marks) What are the three coordinates, in terms of qs, Qy, and az, of the head of the unit vector when it lies in the xz-plane (the question marks in the figure)? Explain why. (b) (4 marks) Let us change our rotation process a little bit. When the unit vector lies in the xz plane, let's rotate it about the y-axis such that it aligns with the positive direction of the x-axis. Derive the corresponding matrix, if possible. (1) (6 marks) We have discussed in class that a rotation around an arbitrary axis can be decomposed into a series of transformations. Look at the following picture that has been discussed in class and whose purpose is to show that we try to rotate the arbitrary axis such that it aligns with the positive direction of the z-axis. Olx ay al Z In the picture, the unit vector whose head is at (Qx, dy, az) is the axis about which the rotation is to be conducted. O, is the angle we rotate the unit vector, about the direction of the x-axis, such that it eventually lies in the xz plane. Then the unit vector is rotated Oy degrees about the direction of the y-axis such that it aligns with the positive direction of the z-axis. (a) (2 marks) What are the three coordinates, in terms of qs, Qy, and az, of the head of the unit vector when it lies in the xz-plane (the question marks in the figure)? Explain why. (b) (4 marks) Let us change our rotation process a little bit. When the unit vector lies in the xz plane, let's rotate it about the y-axis such that it aligns with the positive direction of the x-axis. Derive the corresponding matrix, if possible