\[\operatorname{curl}\mathbf{F}=\nabla\times\mathbf{F}=\begin{vmatrix}\mathbf{i}%
&\mathbf{j}&\mathbf{k}\\
\displaystyle{\frac{\partial}{\partial x}}&\displaystyle{\frac{\partial}{%
\partial y}}&\displaystyle{\frac{\partial}{\partial z}}\\
F_{1}&F_{2}&F_{3}\end{vmatrix}\\
=\left(\frac{\partial F_{3}}{\partial y}-\frac{\partial F_{2}}{\partial z}%
\right)\mathbf{i}+\left(\frac{\partial F_{1}}{\partial z}-\frac{\partial F_{3}%
}{\partial x}\right)\mathbf{j}+\left(\frac{\partial F_{2}}{\partial x}-\frac{%
\partial F_{1}}{\partial y}\right)\mathbf{k}.\]