# What is the angle between <9,-5,1 >  and < -7,4,2 >?

Jul 19, 2018

The angle is $= {160.5}^{\circ}$

#### Explanation:

The angle between $2$ vectors $\vec{A}$ and $\vec{B}$ is given by the dot product definition.

vecA.vecB=∥vecA∥*∥vecB∥costheta

Where $\theta$ is the angle between $\vec{A}$ and $\vec{B}$

The dot product is

vecA.vecB=〈9,-5,1〉.〈-7,4,2〉=-63-20+2=-81

The modulus of $\vec{A}$= ∥〈9,-5,1〉∥=sqrt(81+25+1)=sqrt107

The modulus of $\vec{B}$= ∥〈-7,4,2〉∥=sqrt(49+16+4)=sqrt69

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-81/(sqrt107*sqrt69)=-0.943

$\theta = \arccos \left(- 0.943\right) = {160.5}^{\circ}$