Question

If `A = <5 ,6 ,-3 >`, `B = <-9 ,6 ,-5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=57.3`º

Explanation:

Let's start calculating `vecC`

`vecC=vecA-VecB=〈5,6,-3〉-〈-9,6,-5〉`
`=〈14,0,2〉`

To calculate the angle `theta` between `vecA` and `vecC`,
we use the dot product definition:

`vecA.vecC=∥vecA∥*∥vecC∥costheta`

The dot product `=〈5,6,-3〉.〈14,0,2〉=70+0-6=64`

The modulus of `vecA=∥〈5,6,-3〉∥=sqrt(25+36+9)=sqrt70`

The modulus of `vecC=∥〈14,0,2〉∥=sqrt(196+0+4)=sqrt200`

`:. cos theta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=64/(sqrt70sqrt200)`

`costheta=0.54`

`theta=57.3`º