Question

If `A = <2 ,4 ,-9 >`, `B = <3 ,0 ,-5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `30`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈2,4,-9〉-〈3,0,-5〉=〈-1,4,-4〉`

The angle between `vecA` and `vecC` is given by the dot product definition.

`vecA.vecC=∥vecA∥*∥vecC∥costheta`

Where `theta` is the angle between `vecA` and `vecC`

The dot product is

`vecA.vecC=〈2,4,-9〉.〈-1,4,-4〉=-2+16+36=50`

The modulus of `vecA`= `∥〈2,4,-9〉∥=sqrt(4+16+81)=sqrt101`

The modulus of `vecC`= `∥〈-1,4,-4〉∥=sqrt(1+16+16)=sqrt33`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=50/(sqrt101*sqrt33)=0.866`

`theta=30`º