Answer
$-3z\textbf{i}$
Work Step by Step
curl $\textbf{F}=\nabla\times\textbf{F}=\nabla\times\langle0,z^{2}-y^{2},-yz\rangle$
$=(\frac{\partial (-yz)}{\partial y}-\frac{\partial (z^{2}-y^{2})}{\partial z})\textbf{i}+(\frac{\partial(0)}{\partial z}-\frac{\partial(-yz)}{\partial x})\textbf{j}+(\frac{\partial(z^{2}-y^{2})}{\partial x}-\frac{\partial(0)}{\partial y})\textbf{k}$
$=(-z-2z)\textbf{i}+(0-0)\textbf{j}+(0-0)\textbf{k}$
$=-3z\textbf{i}$
