Commutes, so

\(\vec{u} \cdot \vec{v} = \vec{v} \cdot \vec{u}\);

distributes over vector addition, so

\(\vec{u} \cdot (\vec{v} + \vec{w}) = \vec{u} \cdot \vec{v} + \vec{u} \cdot \vec{w}\);

associates with respect to scalar multiplication, so

\((c \vec{u}) \cdot \vec{v} = c (\vec{u} \cdot \vec{v}) = \vec{u} \cdot (c \vec{v})\).