Vector dot product

The vector dot product - sometimes called the scalar product, or inner product is defined as follows:

Definition

Given two vectors in a finite vector space $a,b\in V$ where $v_i$ denotes the $i^\text{th}$ element of $v$, the dot product is defined as follows:

$$a\cdot b=\sum^n_{i=1}a_ib_i$$

Other forms

Angle between vectors

$$a\cdot b=\|a\|\|b\|\cos(\theta)$$ where $\theta$ is the angle between the vectors $a$ and $b$