Question

If `A = <5 ,4 ,3 >`, `B = <2 ,-7 ,5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `49.6`º

Explanation:

Let's start by calculating `vecC=vecA-vecB=〈5,4,3〉-〈2,-7,5〉`

`vecC=〈3,11,-2〉`

To calculate the angle, we use the dot productt definition,

`vecA.vecC=∥〈5,4,3〉∥*∥〈3,11,-2〉∥*costheta`
where `theta` is the angle between the 2 vectors

`vecA.vecC=〈5,4,3〉.〈3,11,-2〉=15+44-6=53`

Modulus of `vecA=∥〈5,4,3〉∥=sqrt(25+16+9)=sqrt50`

Modulus of `vecC=∥〈3,11,-2〉∥=sqrt(9+121+4)=sqrt134`

`:. cos theta=53/(sqrt50*sqrt134=0.65`

`theta=49.6`º