# What is the angle between <8,7,6>  and <-1,6,1>?

Jan 18, 2017

The angle is $57.9$º

#### Explanation:

The angle between $\vec{A}$ 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=〈8,7,6〉.〈-1,6,1〉=-8+42+6=40

The modulus of $\vec{A}$= ∥〈8,7,6〉∥=sqrt(64+49+36)=sqrt149

The modulus of $\vec{B}$= ∥〈-1,6,1〉∥=sqrt(1+36+1)=sqrt38

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=40/(sqrt38*sqrt149)=0.53

$\theta = 57.9$º