Question

If `A = <1 ,6 ,9 >`, `B = <-9 ,4 ,-8 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=35.6`º

Explanation:

Let's start by calculating `vecC`

`vecC=vecA-vecB=〈1,6,9〉-〈-9,4,-8〉=〈10,2,17〉`

The angle `theta` is given by the dot product definition

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

`vecA.vecC=〈10,2,17〉.〈1,6,9〉=10+12+153=175`

The modulus of `vecA=∥vecA∥=∥〈1,6,9〉∥=sqrt(1+36+81)=sqrt118`

The modulus of `vecC=∥vecC∥=∥〈10,2,17〉∥=sqrt(100+4+289)=sqrt393`

Therefore, `costheta=175/(sqrt118*sqrt393)=0.81`

`theta=35.6`º