Question

What is the angle between `<-2,7,-1>` and `<6,-1,4 >`?

Answer 1

The angle is `=115.5`º

Explanation:

The angle between `vecu` and `vecv` is given by the dot product definition.

`vecu.vecv=∥vecu∥*∥vecv∥costheta`

Where `theta` is the angle between `vecu` and `vecv`

The dot product is

`vecu.vecv=〈-2,7,-1〉.〈6,-1,4〉=-12-7-4=-23`

The modulus of `vecu`= `∥〈-2,7,-1〉∥=sqrt(4+49+1)=sqrt54`

The modulus of `vecv`= `∥〈6,-1,4〉∥=sqrt(36+1+16)=sqrt53`

So,

`costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)=-23/(sqrt54*sqrt53)=-0.43`

`theta=115.5`º