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$$\nabla \times F:=\left|\begin{array}{ccc}{e}_x& e_y& e_z\\ \frac{\partial }{\partial x}& \frac{\partial }{\partial y}& \frac{\partial }{\partial z}\\ F_x& F_y& F_z\end{array}\right|=\left(\frac{\partial F_z}{\partial y}-\frac{\partial F_y}{\partial z}\right)e_x+\left(\frac{\partial F_x}{\partial z}-\frac{\partial F_z}{\partial x}\right)e_y+\left(\frac{\partial F_y}{\partial x}-\frac{\partial F_x}{\partial y}\right)e_z$$

In the above, $e_x,e_y,e_z$ are three orthogonal axis $F:{\mathbb{R}}^3\to {\mathbb{R}}^3$ is a 3-dimensional Vector field $|\cdot |$ is the determinant of a matrix $\nabla :=(\frac{\partial }{\partial x_1},\cdots ,\frac{\partial }{\partial x_n})$ is the Del or Nabla vector Operator