# 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 [ilmath]a,b\in V[/ilmath] where [ilmath]v_i[/ilmath] denotes the [ilmath]i^\text{th} [/ilmath] element of [ilmath]v[/ilmath], 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 [ilmath]\theta[/ilmath] is the angle between the vectors [ilmath]a[/ilmath] and [ilmath]b[/ilmath]