Question

If `A = <2 ,3 ,6 >`, `B = <5 ,1 ,7 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=103.2`º

Explanation:

Let's start by calculating `vecC`

`vecC=vecA-vecB=〈2,3,6〉-〈5,1,7〉=〈-3,2,-1〉`

The angle betwwen two vectors is given by the dot product.

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

Where `theta` is the angle between the 2 vectors.

The dot product is

`vecA.vecC=〈2,3,6〉.〈-3,2,-1〉=-6+6-6=-6`

The modulus of `vecA` is
`∥vecA∥=∥〈2,3,6〉∥=sqrt(4+9+36)=sqrt49=7`

The modulus of `vecC` is
`∥vecC∥=∥〈-3,2,-1〉∥=sqrt(9+4+1)=sqrt14`

Therefore,
`costheta=-6/(7sqrt14)=-0.23`

`theta=103.2`º