# What is the dot product of two vectors that are perpendicular?

The dot of two vectors is given by the sum of its correspondent coordinates multiplied. In mathematical notation:
let $v = \left[{v}_{1} , {v}_{2} , \ldots , {v}_{n}\right]$ and $u = \left[{u}_{1} , {u}_{2} , \ldots , {u}_{n}\right]$,
Dot product:
$v \cdot u =$
$\sum {v}_{i} . {u}_{i} = \left({v}_{1} . {u}_{1}\right) + \left({v}_{2} . {u}_{2}\right) + \ldots + \left({v}_{n} . {u}_{n}\right)$

and angle between vectors:
$\cos \left(\theta\right) = \frac{v \cdot u}{| v | | u |}$

Since the angle between two perpendicular vectors is $\frac{\pi}{2}$, and it's cosine equals 0:
$\frac{v \cdot u}{| v | | u |} = 0 \therefore v \cdot u = 0$

Hope it helps.