# What is the angle between <-5,-3,6 >  and <3,9,-9> ?

Mar 19, 2018

The angle is $= {151.3}^{\circ}$

#### 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=〈-5,-3,6〉.〈3,9,-9〉=-15-27-54=-96

The modulus of $\vec{A}$= ∥〈-5,-3,6〉∥=sqrt(25+9+36)=sqrt70

The modulus of $\vec{B}$= ∥〈3,9,-9〉∥=sqrt(9+81+81)=sqrt171

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-96/(sqrt70*sqrt171)=-0.877

$\theta = \arccos \left(- 0.877\right) = {151.3}^{\circ}$