Dot product is denoted as .

Geometric Definition

\mathbf{u} \cdot \mathbf{v}= \begin{cases}|\mathbf{u}||\mathbf{v}| \cos [\mathbf{u}, \mathbf{v}], & \text { if } \mathbf{u} \neq \mathbf{0} \text { and } \mathbf{v} \neq \mathbf{0} \ 0, & \text { if } \mathbf{u}=\mathbf{0} \text { or } \mathbf{v}=\mathbf{0}\end{cases}

If two vectors are orthogonal, then their dot product is :

The dot product can be getting from the Euclidean norm.

Properties

Dot product satisfies the following properties: