Question

If `A = <-5 ,2 ,1 >`, `B = <-8 ,4 ,9 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=124.2`º

Explanation:

Let's calculate `vecC`

`vecC=vecA-vecB`

Therefore, `vecC=〈-5,2,1〉-〈-8,4,9〉=〈3,-2,-8〉`

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

`vecA.vecC=∥vecA∥.∥vecC∥costheta`

The dot product is
`vecA.vecC=〈-5,2,1〉.〈3,-2,-8〉=-15-4-8=-27`

The modulus of `vecA=∥〈-5,2,1〉∥=sqrt(25+4+1)=sqrt30`

The modulus of `vecC=∥〈3,-2,-8〉∥=sqrt(9+4+64)=sqrt77`

Therefore, `costheta=vecA.vecC/(∥vecA∥.∥vecC∥)`

`=-27/(sqrt30*sqrt77)=-0.56`

`theta=124.2`º