Consider the function V(x,y,z)=x 4
+y 5
+z 6
in three dimensions. Calculate the following quantities and indicate which of these is a vector and which is a scalar. (a) ∇(∇ 2
V) (b) (∇V×∇V)⋅(∇V) (c) ∇×(∇×(V i
^
)) where i
^
is the unit vector in the x-direction. (d) ∇ 2
(∇V) (c) ∇(∇V⋅∇V)