Question

If `A = <2 ,2 ,5 >`, `B = <5 ,-7 ,8 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=93º`

Explanation:

Let's start by calculating `vecC=〈2,2,5〉-〈5,-7,8〉=〈-3,9,-3〉`
The angle `theta`is given by `vecA.vecC=∥vecA∥∥vecC∥*costheta`
So `costheta=(vecA.vecC)/(∥vecA∥∥vecC∥)`

`vecA.vecC=〈2,2,5〉.〈-3,9,-3〉=-6+18-15=-3`
`∥vecA∥=∥〈2,2,5〉∥=sqrt(4+4+25)=sqrt33`
`∥vecC∥=∥〈-3,9,-3〉∥=sqrt(9+81+9)=sqrt99`
`costheta=-3/(sqrt33.sqrt99)=-0.0524`
`theta=93º`