Solution
= Solution
The Cartesian <curl> is obtained by cross-differentiating the components:
$$
\boxed{\nabla\times\mathbf F=(\partial_yF_z-\partial_zF_y,\ \partial_zF_x-\partial_xF_z,\ \partial_xF_y-\partial_yF_x)=(-2yz,4xz^2,0).}
$$
= Solution
The Cartesian <curl> is obtained by cross-differentiating the components:
$$
\boxed{\nabla\times\mathbf F=(\partial_yF_z-\partial_zF_y,\ \partial_zF_x-\partial_xF_z,\ \partial_xF_y-\partial_yF_x)=(-2yz,4xz^2,0).}
$$