Which vector field is irrotational (i.e., ∇×F=0\nabla \times \mathbf{F} = \mathbf{0}∇×F=0)?
F(x,y,z)=⟨y+z,x+z,x+y⟩\mathbf{F}(x,y,z) = \langle y+z, x+z, x+y \rangleF(x,y,z)=⟨y+z,x+z,x+y⟩
F(x,y,z)=⟨z,0,−x⟩\mathbf{F}(x,y,z) = \langle z, 0, -x \rangleF(x,y,z)=⟨z,0,−x⟩
F(x,y,z)=⟨y,−x,0⟩\mathbf{F}(x,y,z) = \langle y, -x, 0 \rangleF(x,y,z)=⟨y,−x,0⟩
F(x,y,z)=⟨yz,xz,xy⟩\mathbf{F}(x,y,z) = \langle yz, xz, xy \rangleF(x,y,z)=⟨yz,xz,xy⟩