Question

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

Answer 1

The angle is `=131.6`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈2,4,-3〉-〈3,4,-5〉=〈-1,0,2〉`

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,-3〉.〈-1,0,2〉=-2+0-6=-8`

The modulus of `vecA`= `∥〈2,4,-3〉∥=sqrt(4+16+9)=sqrt29`

The modulus of `vecC`= `∥〈-1,0,2〉∥=sqrt(1+0+4)=sqrt5`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=-8/(sqrt29*sqrt5)=-0.664`

`theta=131.6`º