How to show this vector field is irrotational?

Question

I have the field: $$\bar a(\bar r)=r \bar c + \frac{(\bar c\cdot \bar r)}{r}\bar r$$ where $$\bar c $$ is a constant vector.

I have worked through the problem and I cant seem to easily show that: $$ \bar \nabla \times \bar a (\bar r ) = 0 $$

I get instead $$-(\hat r\times\bar c)$$. Any help would be most appreciated!

Answer 1

Hint: compute $\mathrm{div}(a(\bar r))$ and show it is not zero.