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:
(Commutativity) (Associativity) - dot production is distributive over the addition (Distributive)
(Positive-definiteness)