Question

If `A = <7 ,-5 ,6 >`, `B = <4 ,4 ,9 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=62.6`º

Explanation:

We start by calculating `vecC`

`vecC=vecA-vecB`

`=〈7,-5,6〉-〈4,4,9〉=〈3,-9,-3〉`

The angle between 2 vectors is given by the dot product.

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

The dot product is `〈7,-5,6〉.〈3,-9,-3〉=21+45-18=48`

The modulus of `vecA=∥〈7,-5,6〉∥=sqrt(49+25+36)=sqrt110`

The modulus of `vecC=∥〈3,-9,-3〉∥=sqrt(9+81+9)=sqrt99`

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)`

`=48/(sqrt110sqrt99)=0.46`

`theta=62.6`º