Question

What is the angle between `<-3,2,0 >` and `<6,-9,8>`?

Answer 1

The angle is `=137.9`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=〈-3,2,0〉.〈6,-9,8〉=-18-18+0=-36`

The modulus of `vecA`= `∥〈-3,2,0〉∥=sqrt(9+4+0)=sqrt13`

The modulus of `vecB`= `∥〈6,-9,8〉∥=sqrt(36+81+64)=sqrt181`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-36/(sqrt13*sqrt181)=-0.742`

`theta=137.9`º