Question

If `A = <4 ,1 ,5 >`, `B = <6 ,2 ,-2 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=68.2^@`

Explanation:

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=〈4,1,5〉.〈6,2,-2〉=24+2-10=16`

The modulus of `vecA`= `∥〈4,1,5〉∥=sqrt(16+1+25)=sqrt42`

The modulus of `vecC`= `∥〈6,2,-2〉∥=sqrt(36+4+4)=sqrt44`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=16/(sqrt42*sqrt44)=0.37`

`theta=68.2^@`