In index notation, this means:
$\epsilon_{ijk} \frac{\partial a_k}{\partial z_j} = 0$
Since this holds for all $i, j, k$, we have:
$\boxed{(\nabla \times a)_{ijk} = 0}$
iv) $\nabla \times (\nabla o) = 0$
This is true if and only if the curl of the gradient of the
Show more…