Could someone please explain to me why $$\nabla (\dot{r}\cdot A)$$ take the following form in index notation? $$\left({\partial A_i\over \partial r^k}-{\partial A_k\over \partial r^i}\right)\dot{r}^i$$
Thanks.
Also, i have read that apparently $(\nabla A)\cdot B\neq B\cdot (\nabla A)=(B\cdot \nabla) A$ which doesn't make sense to me because I thought that the dot product of vectors should be symmetric! Could someone please explain? Thanks again.