# What is the angle between <5,7,1> and <5,1,7> ?

Jan 18, 2017

The angle is $58.7$º

#### Explanation:

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

vecA.vecC=∥vecA∥*∥vecB∥costheta

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

The dot product is

vecA.vecB=〈5,7,1〉.〈5,1,7〉=25+7+7=39

The modulus of $\vec{A}$= ∥〈5,7,1〉∥=sqrt(25+49+1)=sqrt75

The modulus of $\vec{C}$= ∥〈5,1,7〉∥=sqrt(15+1+49)=sqrt75

So,

costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=39/(sqrt75*sqrt75)=39/75=0.52

$\theta = 58.7$º