# What is the angle between <-2,7,-1>  and <6,-1,4 >?

Feb 9, 2017

The angle is $= 115.5$º

#### Explanation:

The angle between $\vec{u}$ and $\vec{v}$ is given by the dot product definition.

vecu.vecv=∥vecu∥*∥vecv∥costheta

Where $\theta$ is the angle between $\vec{u}$ and $\vec{v}$

The dot product is

vecu.vecv=〈-2,7,-1〉.〈6,-1,4〉=-12-7-4=-23

The modulus of $\vec{u}$= ∥〈-2,7,-1〉∥=sqrt(4+49+1)=sqrt54

The modulus of $\vec{v}$= ∥〈6,-1,4〉∥=sqrt(36+1+16)=sqrt53

So,

costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)=-23/(sqrt54*sqrt53)=-0.43

$\theta = 115.5$º