10.A. Consider the vector field F = (r, y, 0). (a) Compute Vx F and V . F. (b) Let C be the closed curve in the plane z = y + 3 lying over the curve r = 2 cos in the ry-plane. Compute Q F . Tds. c (c) Compute the flux of F out of the cylinder a + y = 4 for -27 S = $ 2x. (d) Compute the flux of F out of the wavy cylinder r = 2 + sin z for -27 $ 2 5 2x. 10.B. Let F(x, y, #) = r Irl G(x, y, 2) = |r 3 be two vector fields, where r = ri + yj + zk. (a) Let S be the sphere of radius 3 centered at the origin. Compute: (i) The flux of F out of S. (ii) The flux of G out of S. (b) Describe a surface T' such that the flux of F through T' equals the flux of G through T. Give an equation for T