\[ \vec{v} \times \vec{w} = \begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ \frac{\partial \vec{v}}{\partial x} & \frac{\partial \vec{v}}{\partial y} & \frac{\partial \vec{v}}{\partial z} \\ \frac{\partial \vec{w}}{\partial x} & \frac{\partial \vec{w}}{\partial y} & \frac{\partial \vec{w}}{\partial z} \\ \end{vmatrix} \]