For the questions that follow, you will need the following objects. ·The surface S, given by the part of +z2-9z? which is above the xy-plane. . The curve C, given by t) =å3t cos(t), t sin(t)) for 0 t 21. . The two-dimensional vector field F, whose vectors are the gradient vectors of S = f(x,y). 1. Sketch some of the level curves of S on the ay-plane, and use these level curves to sketch the vector field F 2. Verify that the curve C lies on the surface S. What is the equation of the curve Cı which is the projection of C on the cy plane? 3. Is Jo, F di zero or nonzero? Explain, using your picture. 4. Calculate F.d 5. Find two non-parallel vectors which are tangent to S at the point ( 0,5). Could your method of finding these vectors be used on other surfaces at other points?