# What is the angle between <-4,2,-1 >  and <-8,0,0> ?

Mar 2, 2017

The angle is $= 29.2$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=〈-4,2,-1〉.〈-8,0,0 〉 = 32

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

The modulus of $\vec{B}$= ∥〈-8,0,0〉∥=sqrt64=8

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=32/(sqrt21*8)=0.87

$\theta = 29.2$º