# What is the angle between <8,-1,2>  and <-4,-1,3>?

Jan 16, 2017

The angle is $= 53.8$º

#### Explanation:

The angle is given by the dot product definition

veca.vecb=∥veca∥*∥vecb∥costheta

Where, $\theta$ is the angle between the 2 vectors

Here, we have

veca=〈8,-1,2〉

vecb=〈-4,-1,3〉

The dot product is 〈8,-1,2〉.〈-4,-1,3〉=-32+1+6=25

The modulus of $\vec{a}$ is =∥〈8,-1,2〉∥=sqrt(64+1+4)=sqrt69

The modulus of $\vec{b}$ is =∥〈-4,-1,3〉∥=sqrt(16+1+9)=sqrt26

Therefore,

costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=25/(sqrt69*sqrt26)=0.59

$\theta = 53.8$º