C10D.3 We can prove that the dot product is distributive as follows. Let šw +. Note that we can think of the dot product υ-s as being li l times the projection of s on u. The figure below shows this projection as well as the projec- tions of w and q on 11. (a) Assume that a, q, and 11 all lie in the same plane. Use the diagram above and a trigonometric identity to (b) Assume that š and iü define the plane of the diagram above, but that w and a no longer necessarily lie in that same plane. Adjust your proof for part (a) to take this into account. C10D.3 We can prove that the dot product is distributive as follows. Let šw +. Note that we can think of the dot product υ-s as being li l times the projection of s on u. The figure below shows this projection as well as the projec- tions of w and q on 11. (a) Assume that a, q, and 11 all lie in the same plane. Use the diagram above and a trigonometric identity to (b) Assume that š and iü define the plane of the diagram above, but that w and a no longer necessarily lie in that same plane. Adjust your proof for part (a) to take this into account.