Question

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

Answer 1

The angle is `=97.5`º

Explanation:

The angle between `vecA` and `vecB` is given by the dot product definition.

`vecA.vecB=∥vecA∥*∥vecB∥costheta`

Where `theta` is the angle between `vecA` and `vecB`

The dot product is

`vecA.vecC=〈-2,4,-3〉.〈-1,0,1〉=2+0-3=-1`

The modulus of `vecA`= `∥〈-2,4,-3〉∥=sqrt(4+16+9)=sqrt29`

The modulus of `vecC`= `∥〈-1,0,1〉∥=sqrt(1+0+1)=sqrt2`

So,

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

`theta=97.5`º