Given a vector function F(x, y,z)= (xy)i+ (yz)j+(xz)k and scalar functions $(x, y,z)= xyz and 9(x,...

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Given a vector function F(x, y,z)= (xy)i+ (yz)j+(xz)k and scalar functions $(x, y,z)= xyz and 9(x, y,z) = x + y+z, (a) Show that V.(F) = 0(VF) +F.(Vø) = 2ø0. (16 marks) (b) Show that, at the point (1,1,1), |V(ø9) =4/3. %3D (9 marks) Given a vector function F(x, y,z)= (xy)i+ (yz)j+(xz)k and scalar functions $(x, y,z)= xyz and 9(x, y,z) = x + y+z, (a) Show that V.(F) = 0(VF) +F.(Vø) = 2ø0. (16 marks) (b) Show that, at the point (1,1,1), |V(ø9) =4/3. %3D (9 marks)