- #1

Erbil

- 57

- 0

## Homework Statement

$$ \overrightarrow {F}=3xz^{2}i+2xyj-x^{2}k $$ $$\phi =3x^{2}-yz $$ are given vector and scalar fields, respectively.

a) $$\quad \operatorname{div}\left( \operatorname{grad}\phi \operatorname{div}\overrightarrow {F}\right) =\quad? $$

b) $$\quad \operatorname{curl}\left( \phi F\right) =\quad? $$

c) $$\quad \operatorname{div}\left( \phi F\right) =\quad? $$

d) $$\quad \overrightarrow {\nabla }\cdot \left( \nabla \phi \times \overrightarrow {F}\right) =\quad? $$

e) $$\quad \nabla \cdot \left( \overrightarrow {F}\nabla \phi \right) =\quad? $$

I know the operations such as the Gradient, Divergence, Curl, and Laplacian. But I don't have an idea what can I do in this kind of problems?

## Homework Equations

http://en.wikipedia.org/wiki/Vector_calculus_identities

## The Attempt at a Solution

a)I found gradient of scalar field and divergence of vector field.Gradient of scalar field is a vector and divergence of vector fields is a scalar.So how can I take the divergence of this?

No idea for others.I think I have to use some formula for calculate these..But which? I don't want to a solution just I want to understand logic.Please help me to figure this:) Then I will try to do it myself.

And also,I'd like to say that I'm sorry for my bad English.