# Definition:Dot Product/Definition 2

## Definition

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 $\pi$.

## Also see

• Results about dot product can be found here.