Vorticity of a vector field \(\vec{B}\) is defined as \(\vec{V}=\vec\nabla \times \vec{B}\). Given \(\vec{B}=k x y z \hat{r}\), where k is a constant, which one of the following is correct?
1
Vorticity is a null vector for all finite x, y, z
2
Vorticity is parallel to the vector field everywhere
3
The angle between vorticity and vector field depends on x, y, z
4
Vorticity is perpendicular to the vector field everywhere