# How do you compute the dot product for <-2, 5>*<-1, -2>?

Sep 3, 2016

$< - 2 , 5 > \cdot < - 1 , - 2 > = - 8$

#### Explanation:

A dot product of 2 vectors is defined as the sum of products of respective coordinates:

$< {x}_{1} , {y}_{1} > \cdot < {x}_{2} , {y}_{2} > = {x}_{1} \cdot {x}_{2} + {y}_{1} \cdot {y}_{2}$

In this example we have:

$< - 2 , 5 > \cdot < - 1 , - 2 > = \left(- 2\right) \times \left(- 1\right) + 5 \times \left(- 2\right) = 2 - 10 = - 8$