Question

If `A = <8 ,3 ,2 >`, `B = <6 ,-4 ,5 >`, and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `63.3º`

Explanation:

The angle between two vectors is given by the dot product.
`veca.vecc=∥veca∥*∥vecc∥costheta`
where `theta` is the angle between the two vectors
`vecc=veca-vecb=〈8,3,2〉-〈6,-4,5〉=〈2,7,-3〉`
The dot product is `veca.vecc=〈8,3,2〉.〈2,7,-3〉=16+21-6=31`
The modulus of `veca` is `=∥veca∥=∥〈8,3,2〉∥=sqrt(64+9+4)=sqrt77`
The modulus of `vecc` is `=∥vecc∥=∥〈2,7,-3〉∥=sqrt(4+49+9)=sqrt62`

So `costheta=31/(sqrt77*sqrt62)=0.449`
`theta=63.3º`