# Question 89959

Mar 22, 2017

The angle is $= 41$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=〈2,3,1〉.〈4,1,2〉=8+3+2=13

The modulus of $\vec{A}$= ∥〈2,3,1〉∥=sqrt(4+9+1)=sqrt14

The modulus of $\vec{B}$= ∥〈4,1,2〉∥=sqrt(16+1+4)=sqrt21

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=13/(sqrt14*sqrt21)=0.758#

$\theta = 41$º