Question

If `A = <2 ,-5 ,-8 >`, `B = <-9 ,4 ,-5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `49.5`º

Explanation:

Let's calculate `vecC`

`vecC=vecA-vecB=〈2,-5,-8〉-〈-9,4,-5〉`

`=〈11,-9,-3〉`

The angle `theta` between `vecA` and `vecC` is calculated from the dot product definition

`vecA.vecC=∥vecA∥*∥vecC∥costheta`

The dot product `vecA.vecC=〈2,-5,-8〉.〈11,-9,-3〉`

`=2*11+5*9+8*3=22+45+24=91`

The modulus of `∥vecA∥=∥〈2,-5,-8〉∥=sqrt(4+25+64)=sqrt93`

The modulus of `∥vecC∥=∥〈11,-9,-3〉∥=sqrt(121+81+9)=sqrt211`

Therefore, `costheta=91/(sqrt93*sqrt211)=0.65`

`theta=49.5`º