Determine if the vector field F⃗=⟨y,x⟩\vec{F} = \langle y, x \rangleF=⟨y,x⟩ is conservative.
Yes, because ∂P∂y=∂Q∂x\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}∂y∂P=∂x∂Q.
No, because ∂P∂x≠∂Q∂y\frac{\partial P}{\partial x} \neq \frac{\partial Q}{\partial y}∂x∂P=∂y∂Q.
Yes, because the divergence is zero.
No, because the curl is non-zero.