Question

What is the angle between `<-5,-3,6 >` and `<3,9,-9>`?

Answer 1

The angle is `=151.3^@`

Explanation:

The angle between `2` vectors, `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=〈-5,-3,6〉.〈3,9,-9〉=-15-27-54=-96`

The modulus of `vecA`= `∥〈-5,-3,6〉∥=sqrt(25+9+36)=sqrt70`

The modulus of `vecB`= `∥〈3,9,-9〉∥=sqrt(9+81+81)=sqrt171`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-96/(sqrt70*sqrt171)=-0.877`

`theta=arccos(-0.877)=151.3^@`