Let ν(x,y,z) = (xi + yj + zk)rk where v, i, j, k are vectors
The k in rk∈ℝ and r=√(x2+y2+z2).
Show that ∇.v=λrk except at r=0 and find λ in terms of k.
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)rk? 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.