# What is the angle between <6 , 5 , 7 >  and  < 3 , 3 , 2 > ?

Feb 12, 2017

The angle is $= 17.2$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=〈6,5,7〉.〈3,3,2〉=18+15+14=47

The modulus of $\vec{A}$= ∥〈6,5,7〉∥=sqrt(36+25+49)=sqrt110

The modulus of $\vec{B}$= ∥〈3,3,2〉∥=sqrt(9+9+4)=sqrt22

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=47/(sqrt110*sqrt22)=0.96

$\theta = 17.2$º