Question

If `A = <6 ,4 ,-7 >`, `B = <3 ,-1 ,0 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=18.2`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈6,4,-7〉-〈3,-1,0〉=〈3,5,-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=〈6,4,-7〉.〈3,5,-7〉=18+20+49=87`

The modulus of `vecA`= `∥〈6,4,-7〉∥=sqrt(36+16+49)=sqrt101`

The modulus of `vecC`= `∥〈3,5,-7〉∥=sqrt(9+25+49)=sqrt83`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=87/(sqrt101*sqrt83)=0.95`

`theta=18.2`º