Question

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

Answer 1

The angle is `56.1`º

Explanation:

Let's calculate `vecC=vecA-vecB=〈2,-5,-8〉-〈-9,4,-2〉@`
`=〈11,-9,-6〉`

To calculate the angle `theta` between the 2 vectors, we use the dot product definition.

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

The dot product is `vecA.vecC=〈2,-5,-8〉.〈11,-9,-2〉`
`=22+45+16=83`

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

The modulus of `vecC` = `∥vecC∥=∥〈11,-9,-6〉∥=sqrt(121+81+36)=sqrt238`

`costheta=83/(sqrt93*sqrt238)=0.56`

`theta=56.1`º