Study guide and 6 practice problems on:

Algebra of dot products

Dot products are distributive: $$\mathbf{x} \cdot ( \mathbf{y} + \mathbf{z}) = \mathbf{x} \cdot \mathbf{y} + \mathbf{x} \cdot \mathbf{z}$$
As a result, the FOIL rule applies: $$(\mathbf{w} + \mathbf{x})\cdot(\mathbf{y} + \mathbf{z}) = \mathbf{w}\cdot \mathbf{y} + \mathbf{w}\cdot \mathbf{z} + \mathbf{x} \cdot \mathbf{y} + \mathbf{x} \cdot \mathbf{z}$$
Dot products are commutative: $$\mathbf{x}\cdot \mathbf{y} = \mathbf{y}\cdot \mathbf{x}$$