Calculate the flux of the rotational field F=∇×⟨xz,yx,zy⟩\mathbf{F} = \nabla \times \langle xz, yx, zy \rangleF=∇×⟨xz,yx,zy⟩ through the unit sphere x2+y2+z2=1x^2+y^2+z^2=1x2+y2+z2=1.
111
000
43π\frac{4}{3}\pi34π
4π4\pi4π