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What is the difference between $ (A\cdot\nabla )B$ and $A(\nabla\cdot B)$, where $A$ and $B$ are two vectors.

My guess is that $ (A\cdot\nabla )B$ means the vector $A$ is being multiplied by the rate of change of $B$ in the direction of $A$. And $A(\nabla\cdot B)$ means vector $A$ is being multiplied by the divergence of $B$.

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    $\begingroup$ Yes, that's it. $\endgroup$
    – user228113
    Jul 2, 2016 at 19:07
  • $\begingroup$ Thank you! Vectors can be confusing! $\endgroup$
    – TLR 7 8 agonist
    Jul 2, 2016 at 19:41

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