Question

If `A = <6 ,4 ,9 >`, `B = <3 ,-1 ,0 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=15.8`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈6,4,9〉-〈3,-1,0〉=〈3,5,9〉`

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=〈6,4,9〉.〈3,5,9〉=18+20+81=119`

The modulus of `vecA`= `∥〈6,4,9〉∥=sqrt(36+16+81)=sqrt133`

The modulus of `vecC`= `∥〈3,5,9〉∥=sqrt(9+25+81)=sqrt115`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=119/(sqrt133*sqrt115)=0.96`

`theta=15.8`º