Question

If `A = <6 ,4 ,-7 >`, `B = <3 ,5 ,2 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=36.6`º

Explanation:

Let's start by calculating

`vecC=vecA-vecB`

`=〈6,4,-7〉-〈3,5,2〉=〈3,-1,-9〉`

To calculate the angle `theta` between `vecA` and `vecC`,

we use the dot product definition

`vecA.vecC=∥vecA∥*∥vecC∥costheta`

The dot product is

`vecA.vecC=〈6,4,-7〉.〈3,-1,-9〉=(18-4+63)=77`

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

The modulus of
`vecC=∥〈3,-1,-9〉∥=sqrt(9+1+81)=sqrt91`

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=77/(sqrt101*sqrt91)=0.8`

`theta=36.6`º