(3) Let the surface S be part of the sphere 3:2 + 312 + 22 = 4 (oriented away from the origin) that lies Within the cylinder 11:2 + 3/2 = 1 and above the plane z = 0, and let 1:. denote the unit normal vector in the direction of the orientation. Let C be the boundary curve of 5'. Consider the vector eld F($, y, z) = $73 + yj + wyzk. (a) Evaluate the line integral / F - T d8 directly, without using Stokes' Theorem, 0 Where T is a unit tangent vector to the curve C. (b) Evaluate the surface integral // (V X F) - n dS directly, without using Stokes' S Theorem. Show all working. Note: You should obtain the same answer in (a) and (b). In this question you are conrming the result of Stokes' Theorem for this particular example