Hey should be a simple check to see if this is correct. I cannot figure out how to enter it into Octave or Wolfram alpha so I need human help :)
Evaluate $\vec\nabla^2 \|\vec x\|^2 $ where $\|\vec x\|^2 = x^2 + y^2 +z^2$ and $\vec\nabla = \hat{\imath}\frac{\partial}{\partial x}+\hat{\jmath}\frac{\partial}{\partial y}+\hat{k}\frac{\partial}{\partial z}$.
I have that $$\vec\nabla \|\vec x\|^2 = 2x\hat i + 2y\hat j + 2z \hat k$$
Then applying the divergence operator (dot product with 'del' or 'nabla') $\vec\nabla\cdot$
$$ \vec\nabla^2 \|\vec x\|^2 = 6 $$ Is that right? It is surprising me that it is an integer.