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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.

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If $A$ is a vector, then $\nabla A$ is a tensor of type 2. So it's not an ordinary dot product. – Zhen Lin Jun 11 '12 at 17:14

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