Question

If `A = <2 ,-7 ,5 >`, `B = <5 ,-7 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=66.1º`

Explanation:

The angle between 2 vectors is given by the dot product.
If we have two vectors `vecA` and `vecC`, then the angle `theta`
is given by `costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)`
`vecC=〈2,-7,5〉-〈5,-7,-1〉=〈-3,0,6〉`
The dot product `〈2,-7,5〉.〈-3,0,6〉=-6+0+30=24`
The modulus of `∥vecA∥=sqrt(4+49+25)=sqrt78`
The modulus of `∥vecC∥=sqrt(9+0+36)=sqrt45`

So `costheta=24/((sqrt78)(sqrt45))=0.41`
`theta= arccos(0.41)=66.1º`