# What is the angle between <2,9,-2>  and <0,3,0 >?

Mar 3, 2017

The angle is $= 17.4$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=〈2,9,-2〉.〈0,3,0 〉 = 27

The modulus of $\vec{A}$= ∥〈2,9,-2〉∥=sqrt(4+81+4)=sqrt89

The modulus of $\vec{B}$= ∥〈0,3,0〉∥=sqrt9=3

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=27/(sqrt89*3)=0.95

$\theta = 17.4$º