Question

If `A = <36 ,1 ,5 >`, `B = <4 ,6 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=0`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`vecC=〈36,1,5〉-〈4,6,-1〉=〈32,-5,6〉`

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=〈36,1,5〉.〈32,-5,6〉=1152-5+30=1177`

The modulus of `vecA`= `∥〈36,1,5〉∥=sqrt(1226+1+25)=sqrt1252`

The modulus of `vecC`= `∥〈32,-5,6〉∥=sqrt(1024+25+36)=sqrt1085`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=1177/(sqrt1252*sqrt1085)=1`

`theta=0`º