Given a vector function F(x,y,z) = (xy)i + ()2)j+(xz)k and scalar functions $(x, y,z) = xyz...

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