Question

What is the angle between `<8,7,6>` and `<-1,6,1>`?

Answer 1

The angle is `57.9`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.vecB=〈8,7,6〉.〈-1,6,1〉=-8+42+6=40`

The modulus of `vecA`= `∥〈8,7,6〉∥=sqrt(64+49+36)=sqrt149`

The modulus of `vecB`= `∥〈-1,6,1〉∥=sqrt(1+36+1)=sqrt38`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=40/(sqrt38*sqrt149)=0.53`

`theta=57.9`º