Definition:Dot Product/Real Euclidean Space

Definition
Let $\mathbf a$ and $\mathbf b$ be vectors in real Euclidean space $\R^n$.

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

 * Equivalence of Definitions of Dot Product