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Properties

• 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

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