Question

If `A = <5 ,2 ,8 >`, `B = <2 ,5 ,6 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=56.4`º

Explanation:

et's start by calculating

`vecC=vecA-vecB`

`vecC=〈5,2,8〉-〈2,5,6〉=〈3,-3,2〉`

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=〈5,2,8〉.〈3,-3,2〉=15-6+16=25`

The modulus of `vecA`= `∥〈5,2,8〉∥=sqrt(25+4+64)=sqrt93`

The modulus of `vecC`= `∥〈3,-3,2〉∥=sqrt(9+9+4)=sqrt22`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=25/(sqrt93*sqrt22)=0.55`

`theta=56.4`º