Question

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

Answer 1

The angle is `=17.4`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=〈2,9,-2〉.〈0,3,0 〉 = 27`

The modulus of `vecA`= `∥〈2,9,-2〉∥=sqrt(4+81+4)=sqrt89`

The modulus of `vecB`= `∥〈0,3,0〉∥=sqrt9=3`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=27/(sqrt89*3)=0.95`

`theta=17.4`º