Question

If `A = <8 ,9 ,4 >`, `B = <6 ,7 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `42.2º`

Explanation:

Let's start by calculating `vecC=〈8,9,4〉-〈6,7,-1〉=〈2,2,5〉`
The the angle is calculated from the definition of the dot product
`vecA.vecC=∣vecA∣∣vecC∣cos theta`
So, `costheta=(vecA.vecC)/(∣vecA∣∣vecC∣)`

`vecA.vecC=〈8,9,4〉.〈2,2,5〉=16+18+20=54`

`∣vecA∣=sqrt(8^2+9^2+4^2)=sqrt161`

`∣vecC∣=sqrt(4+4+25)=sqrt33`

`costheta=54/(sqrt161*sqrt33)=0.741`

`theta=42.2º`