\begin{definition}[Definition:Dot Product/Definition 2]
Let $\mathbf a$ and $\mathbf b$ be vectors in a vector space $\mathbf V$.
The '''dot product''' of $\mathbf a$ and $\mathbf b$ is defined as:
:$\mathbf a \cdot \mathbf b = \norm {\mathbf a} \, \norm {\mathbf b} \cos \angle \mathbf a, \mathbf b$
where:
:$\norm {\mathbf a}$ denotes the length of $\mathbf a$
:$\angle \mathbf a, \mathbf b$ is the angle between $\mathbf a$ and $\mathbf b$, taken to be between $0$ and $\pi$.
\end{definition}