Let (x, y, z) and p(x, y, z) be general scalar functions, and let a general vector function be A(x, y,z)= 4,(x, y,z)i+ A,(x, y,z)j+ A,(x, y,z)k. (a) Prove, using the definitions of V,V. and Vx (i.e., grad, div and curl), that i) V(p) = $(V p) + 9(V); [4 marks] ii) V.(Vx A) = 0. [6 marks] (10 marks) (b) Given the particular scalar function (x, y, z) = 3x'y+ y z', i) show that V x (V) =0; [6 marks] ii) find V.(V) at the point (0,1,2); [3 marks] iii) find a unit normal to the surface (x, y, z) =-2 at the point (1,-2,1). [6 marks]