Given the vector field F(x,y,z)=⟨y2z,2xyz+z,xy2−y⟩\mathbf{F}(x,y,z) = \langle y^2z, 2xyz + z, xy^2 - y \rangleF(x,y,z)=⟨y2z,2xyz+z,xy2−y⟩, compute the curl ∇×F\nabla \times \mathbf{F}∇×F.
⟨−2,0,0⟩\langle -2, 0, 0 \rangle⟨−2,0,0⟩
⟨0,y2,2yz⟩\langle 0, y^2, 2yz \rangle⟨0,y2,2yz⟩
⟨2xy,y2,2yz⟩\langle 2xy, y^2, 2yz \rangle⟨2xy,y2,2yz⟩
⟨2xy−2y,y2−1,0⟩\langle 2xy - 2y, y^2 - 1, 0 \rangle⟨2xy−2y,y2−1,0⟩