Question 705031

Calculating the curl of $\vec{B} = kxyz\hat{r}$ in spherical coordinates leads to a vector with components only in the $\hat{\theta}$ and $\hat{\phi}$ directions. Since the original field $\vec{B}$ only has a component in the radial $\hat{r}$ direction, the dot product $\vec{\omega} \cdot \vec{B} = 0$, meaning the vorticity is perpendicular to the vector field.