solved Q4

Q4 (a) If F = 3zi + 4x/ + 2yk and the boundary of the portion of the paraboloid for which z 2 0. C is the interaction of the paraboloid, z =4 -x2 - y? and xy -plane with a counterclockwise orientation looking down the z -axis. Evaluate F . dr by using the Stoke's Theorem. (13 marks) (b) Let F(x, y, z) = -2yi - 3zj - 5xk and C be the circle x2 + y? =9 that forms the boundary of o in the xy -plane where o is the portion of the paraboloid, z =9 - x2 - y? for which z 2 0. (n is pointing outward) (i) Evaluate F.dr (5 marks) (ii) Evaluate | (curl F). nds S (5 marks) (iii) State your conclusion from the answers in parts (i) and (ii). (2 marks)