Let F(x,y,z)=⟨−y3,x3,0⟩\mathbf{F}(x, y, z) = \langle -y^3, x^3, 0 \rangleF(x,y,z)=⟨−y3,x3,0⟩ be a 3D vector field. Find the curl of F\mathbf{F}F.
⟨0,0,3x2+3y2⟩\langle 0, 0, 3x^2 + 3y^2 \rangle⟨0,0,3x2+3y2⟩
⟨0,0,3x2−3y2⟩\langle 0, 0, 3x^2 - 3y^2 \rangle⟨0,0,3x2−3y2⟩
⟨3x2,3y2,0⟩\langle 3x^2, 3y^2, 0 \rangle⟨3x2,3y2,0⟩
⟨0,0,0⟩\langle 0, 0, 0 \rangle⟨0,0,0⟩