3. (a) Consider the vector field F(x, y.z) = (e' siny - yz) i + (e' cosy - x2) )+ (2 - xy)k. (i) Show that the vector field F is conservative. (in) Determine the potential function f (x, y,z) for the vector field F. (iii) Hence, or otherwise, evaluate the work done by the vector field F along the line segment from the point (1, 0, 1) to the point (2, m, -1). (9 marks) (b) Evaluate the line integral along a closed path C for the vector field F(x, y) = (-xy)i+ (x]) ). If we take the domain of the integral to be the disk R: x' + y's a and its bounding circle Cas the closed path. (7 marks) (c) Verify Stokes' Theorem F . = [[(vxF).ndo for the vector field F(x, y, z) = (2z - y)i+ (x+2) ) + (3x -2y). The / is the outward pointing unit normal, S is the surface of the paraboloid defined by z = 9 - x3 - y', and = 20. (9 marks)