\[\vec\nabla\times\vec F = \left({\partial F_z\over\partial y} - {\partial F_y\over\partial z}\right){\bf i} + \left({\partial F_x\over\partial z} - {\partial F_z\over\partial x}\right){\bf j} + \left({\partial F_y\over\partial x} - {\partial F_x\over\partial y}\right){\bf k} \]

\[\vec\nabla\times\vec F = \left({\partial F_z\over\partial y} - {\partial F_y\over\partial z}\right){\bf i} + \left({\partial F_x\over\partial z} - {\partial F_z\over\partial x}\right){\bf j} + \left({\partial F_y\over\partial x} - {\partial F_x\over\partial y}\right){\bf k} \]

\[\vec\nabla\times\vec F = \left({\partial F_z\over\partial y} - {\partial F_y\over\partial z}\right){\bf i} + \left({\partial F_x\over\partial z} - {\partial F_z\over\partial x}\right){\bf j} + \left({\partial F_y\over\partial x} - {\partial F_x\over\partial y}\right){\bf k} \]

\[\vec\nabla\times\vec F = \left({\partial F_z\over\partial y} - {\partial F_y\over\partial z}\right){\bf i} + \left({\partial F_x\over\partial z} - {\partial F_z\over\partial x}\right){\bf j} + \left({\partial F_y\over\partial x} - {\partial F_x\over\partial y}\right){\bf k} \]

\[\vec\nabla\times\vec F = \left({\partial F_z\over\partial y} - {\partial F_y\over\partial z}\right){\bf i} + \left({\partial F_x\over\partial z} - {\partial F_z\over\partial x}\right){\bf j} + \left({\partial F_y\over\partial x} - {\partial F_x\over\partial y}\right){\bf k} \]