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

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1. Oct 12, 2016

Dave-o

1. The problem statement, all variables and given/known data
∇ . r = 3, ∇ x r = 0

2. Relevant equations

3. The attempt at a solution
So far I've gotten up to ∇(∇^2 r)

2. Oct 12, 2016

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.

3. Oct 12, 2016

Dave-o

1. The problem statement, all variables and given/known data

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

2. Relevant equations

∇ . r^ = 3, ∇ x r^ = 0, ∇r = r^ / r

3. The attempt at a solution
From the 3rd equation I got ∇( ∇ . ∇r) => ∇(∇^2 r)

I don't know where to go from there

4. Oct 12, 2016

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.