My problem is simple : given a particle of mass $m$, charge $q$ and velocity $\bf{v}$. If $\bf{A}$ denotes the magnetic potential satisfying $\bf{B}= \nabla \times \bf{A}$. 
I want to etablish the laws of motion in the theory of special relativity for this particle. 

And the problem is that I need to compute $\nabla (\bf{v} \cdot \bf{A})$. 

I read on several textbooks that : $$\nabla (\bf{v} \cdot \bf{A}) = \bf{v} \times (\nabla \times \bf{A}) + (\bf{v} \cdot \nabla) \bf{A} $$

The problem is that the general formula according to wikipedia is $$\nabla (\bf{v} \cdot \bf{A}) = \bf{v} \times (\nabla \times \bf{A}) + \bf{A} \times (\nabla \times \bf{v})+ (\bf{v} \cdot \nabla) \bf{A} + (\bf{A} \cdot \nabla) \bf{v} $$

[with general vectors $\bf{v}$ and $\bf{A}$]

So I don't understand why $\bf{A} \times (\nabla \times \bf{v})+(\bf{A} \cdot \nabla) \bf{v} =0$ if one does not make any other assumption over $\bf{v}$ and $\bf{A}$. 

I think people here have encouter this prolem so please if you walk by and know, just give me a hint of a link.