17. If f(x, y, z) and g(x, y, z) are continuously differentiable scalar functions defined over the oriented surface S with boundary curve C, prove that do [] (V Vg) n d = f Vg dr. S C 18. Suppose that V F = V F2 and V F V F2 and VX F = V F over a re- gion D enclosed by the oriented surface S with outward unit normal n and that F n = F2n on S. Prove that F = F2 throughout D. 19. Prove or disprove that if V F = 0 and V x F = 0, then F = 0.