Question: For the given vector function:
$$\vec{F}(x,y,z)=xz\vec{i}+y\vec{j}+y^2\vec{k}$$
Compute the expression:
$$ (\delta _{3l}\delta _{jm}-\delta _{3m}\delta _{jl}) \frac{\partial^2F_m}{\partial x_j\partial x_l} $$
at the point P=(1,0,1)
I understand for a vector field $\textbf{F}$, the curl of the curl is defined by $$\nabla\times\left(\nabla\times\textbf{F}\right)=\nabla\left(\nabla\cdot\textbf{F}\right)-\nabla^2\textbf{F}$$ where $\nabla$ is the usual del operator and $\nabla^2$ is the vector Laplacian.
I worked out so far that $ (\delta _{3l}\delta _{jm}-\delta _{3m}\delta _{jl}) $ is equal too $\varepsilon _{i3j}\varepsilon _{ilm}$
But i'm confused on how to go from here, if anyone can help - would be greatly appreciated.