# What is the angle between <-2,4,-3>  and <-1,0,1>?

Jan 22, 2017

The angle is $= 97.5$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.vecC=〈-2,4,-3〉.〈-1,0,1〉=2+0-3=-1

The modulus of $\vec{A}$= ∥〈-2,4,-3〉∥=sqrt(4+16+9)=sqrt29

The modulus of $\vec{C}$= ∥〈-1,0,1〉∥=sqrt(1+0+1)=sqrt2

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-1/(sqrt29*sqrt2)=-0.1313

$\theta = 97.5$º