Answer to Question #45870 in Vector Calculus for Mike

Question

1.) For the scalar potential function φ = (x^2 + y^2 + z^2)^2 and the velocity vector field u=(y^2, z, x^2) calculate the following vector quantities:
a.) ∇φ ; ∇⋅ u
b.) (∇^2)φ = (∇⋅ ∇)φ ; (∇^2)u
c.) ∇ × u
where u is a vector, and the vector operator ∇ = ∂/∂x , ∂/∂y, ∂/∂z)