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## Homework Statement

Let

**ν**(x,y,z) = (x

**i**+ y

**j**+ z

**k**)r

^{k}where v, i, j, k are vectors

The k in r

^{k}∈ℝ and r=√(x

^{2}+y

^{2}+z

^{2}).

Show that ∇.

**v**=λr

^{k}except at r=0 and find λ in terms of k.

## Homework Equations

As far as I understand it, ∇.

**v**=∂/∂x

**i**+ ∂/∂y

**j**+ ∂/∂z

**k**, but this may very well be wrong.

## The Attempt at a Solution

That would mean that ∇.

**v**= (

**i**+

**j**+

**k**)r

^{k}? So λ= i+j+k. And the as to finding λ in terms of k, no idea! I don't know how to manipulate an equation with a ∇.

**v**in it.