Question

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

Answer 1

The angle is `=70.8º`

Explanation:

Let's calculate `vecC`

`vecC=vecA-vecB`

`vecC=〈4,3,-7〉-〈5,7,-3〉=〈-1,-4,-4〉`

The angle between the `vecA` and `vecC` is given by the dot product.

`vecA.vecC=∥vecA∥*∥vecC∥*costheta`

The dot product is

`vecA.vecC=〈4,3,-7〉.〈-1,-4,-4〉=(-4-12+28)=12`

The modulus of `vecA` is `=∥vecA∥=∥〈4,3,-7〉∥=sqrt(16+9+49)=sqrt74`

The modulus of `vecC` is `=∥vecC∥=∥〈-1,-4,-4〉∥=sqrt(1+1+16)=sqrt18`

Therefore,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=12/(sqrt74sqrt18)=0.329`

`theta=70.8º`