Question

If `A = <7 ,-8 ,-2 >`, `B = <4 ,-8 ,5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=64.9`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈7,-8,-2〉-〈4,-8,5〉=〈3,0,-7〉`

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=〈7,-8,-2〉.〈3,0,-7〉=21+0+14=35`

The modulus of `vecA`= `∥〈7,-8,-2〉∥=sqrt(49+64+4)=sqrt117`

The modulus of `vecC`= `∥〈3,0,-7〉∥=sqrt(9+0+49)=sqrt58`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=35/(sqrt117*sqrt58)=0.425`

`theta=64.9`º