A train and a fly are speeding towards each other along a railroad track. A camera mounted on the front of the train has focal length f = 1, and coordinate axes x-y-z oriented with respect to world X-Y-Z axes as shown in the picture below. The train is moving with constant world velocity V_train = (100, 0, 0). The fly is moving with constant world velocity V_fly = (-10, 0, d0). What is the rotation matrix that rotates world coordinate X-Y-Z axes into alignment with the camera coordinate x-y-z axes? What is the FOE of the train's motion wrt the camera view from the train? Recall that the FOE is the 2D location in the film plane where the 3D velocity vector would pass through l intersect the film plane. That is, if velocity vector was (v_x, v_y, v_z), then the FOE in the image is (f v_x/v_z, f v_y/v_z). What is the relative velocity of the fly as seen from the moving camera? At the last moment, the fly takes evasive action, and veers off with new constant world velocity V_fly = (-20 10 60). What is the new relative velocity of the fly as seen from the moving camera? If the train also took evasive action to avoid the fly by suddenly veering off with new constant velocity V_train = (100, 200, 300) and no change in orientation (never mind that it would be physically impossible for a train to do this; it is a very special train), what would the FOE of the train's new motion be wrt the camera view from the train?