Question

If `A = <6 ,8 ,2 >`, `B = <7 ,1 ,-4 >` and `C=A-B`, what is the angle between A and C?

Answer 1

THe angle is `49`º

Explanation:

Let's start by calculating `vecC`

`vecC=vecA-vecB=〈6,8,2〉-〈7,1,-4〉=〈-1,7,6〉`

The angle between 2 vectors is given by the dot product.

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

where, `theta` is the angle between the two vectors.

The dot product is
`=〈-1,7,6〉.〈6,8,2〉=-6+56+12=62`

The modulus of `vecA` is

`∥vecA∥=∥〈6,8,2〉∥=sqrt(36+64+4)=sqrt104`

The modulus of `vecC` is

`∥vecC∥=∥〈-1,7,6〉∥=sqrt(1+49+36)=sqrt86`

Therefore,
`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=62/(sqrt104*sqrt86)=0.66`

`theta=49`º