# Vector Difference

I realize this may be an elementary question however I want to make sure I am not mistaken in my analysis.

I am uncertain what property of $$\nabla$$ means these two terms are not equal. (It came up in a fluid mechanics proof related to vorticity). (note: $$u, v$$ are vectors).

From continuity: $$\nabla \cdot u = 0$$

Which means: $$w( \nabla \cdot u)=0$$

However: $$(u \cdot \nabla)w \neq 0$$

Is it because the divergence will always act on the RH element first?

Any help is much appreciated