# Physical intuition on bivector in fluid dynamics

Reading the M. S. Howe's Theory of Vortex Sound I've ran into this exoression and equation:

Let $v_A$ denote the fluid velocity at a point A at $x$. The velocity $v_B$ at a neighbouring point B at $x + \delta x$ can be written: $v_B \approx v_A + (\delta x \cdot\nabla)v = v_A + \frac{1}{2}\omega \ \wedge \ \delta x + \frac{1}{2}\nabla (e_{ij} \delta x_i \delta x_j)$

I don't follow from where we got the wedgle in the second term of last expression and why is that not simple "$\times$". What is the difference here?