# What is the difference between $(A\cdot\nabla )B$ and $A(\nabla\cdot B)$?

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 $B$.

• Yes, that's it.
– user228113
Jul 2, 2016 at 19:07
• Thank you! Vectors can be confusing! Jul 2, 2016 at 19:41