# What is the angle between <6,-2,9>  and  < -2,1,-8 > ?

Mar 20, 2018

The angle is $= {160.3}^{\circ}$

#### 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=〈6,-2,9〉.〈-2,1,-8〉=-12-2-72=-86

The modulus of $\vec{A}$= ∥〈6,-2,9〉∥=sqrt(36+4+81)=sqrt121=11

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

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-86/(11*sqrt69)=-0.94

$\theta = \arccos \left(- 0.94\right) = {160.3}^{\circ}$