Evaluate: ∇(∇r(hat)/r) where r is a position vector

[Dave-o]

Homework Statement

∇ . r = 3, ∇ x r = 0

Homework Equations

The Attempt at a Solution

So far I've gotten up to ∇(∇^2 r)

 

[kuruman]

Hi Dave-o and welcome to PF. You need to provide more details about what the problem is, the relevant equations and your attempt at a soluton before we can help you.

 

[Dave-o]

Homework Statement

Not using any Cartesian or any other coordinates but rather the facts that (see equations, r^ is the position vector)..
Evaluate:
∇( ∇ . (r^ / r))

Homework Equations

∇ . r^ = 3, ∇ x r^ = 0, ∇r = r^ / r

The Attempt at a Solution

From the 3rd equation I got ∇( ∇ . ∇r) => ∇(∇^2 r)

I don't know where to go from there

 

[kuruman]

Are you allowed to use vector analysis identities? What comes to mind is ## \vec{\nabla} \cdot (\phi \vec{A})=\phi \vec{\nabla} \cdot \vec{A}+\vec{A} \cdot \vec{\nabla}\phi##. You can use this to find the term in parentheses and then take its gradient. You should also be allowed to use the expression for the gradient of 1/r.