Find ∇×F\nabla \times \mathbf{F}∇×F where F(x,y,z)=⟨yz,xz,xy⟩\mathbf{F}(x,y,z) = \langle yz, xz, xy \rangleF(x,y,z)=⟨yz,xz,xy⟩.
⟨x−y,y−z,z−x⟩\langle x-y, y-z, z-x \rangle⟨x−y,y−z,z−x⟩
⟨y−z,z−x,x−y⟩\langle y-z, z-x, x-y \rangle⟨y−z,z−x,x−y⟩
⟨0,0,0⟩\langle 0, 0, 0 \rangle⟨0,0,0⟩ (the zero vector)
⟨x+y,y+z,z+x⟩\langle x+y, y+z, z+x \rangle⟨x+y,y+z,z+x⟩