(a) Verify, for the scalar field o(x, y, z) = sin(x²yz), that V x Vo = 0. (b) If F= y²zi - 3x²zj + x³y²k and p = √ayz², verify the following vector identity, V OF Vo F + ØV.F. (c) A vector field is given by F = 2xye* cos(x²y)i +x²e³ cos(x²y)j + e* sin(x²y)k. i. Show that the vector field F is irrotational, that is, Vx F = 0. ii. Determine a scalar potential o such that F = Vo. > of 2 (5+5+(4+6)= 20 marks) 7-2 ZOOM + ✓