Question

How do you find the angel between u=<-6,-2> and v=<2,12>?

Answer 1

The angle is `117.9`º

Explanation:

The angle is given by the dot product definition

`vecu.vecv=∥vecu∥*∥vecv∥*costheta`

Where `theta` is the angle between the 2 vectors.

The dot prduct is `vecu.vecv =〈-6,-2〉.〈2,12〉=(-12-24)=-36`

The modulus of `vecu=∥〈-6,-2〉∥=sqrt(34+4)=sqrt40`

The modulus of `vecv=∥〈2,12〉∥=sqrt(4+144)=sqrt148`

Therefore, `costheta=vecu.vecv/(∥vecu∥*∥vecv∥)`

`=-36/(sqrt40*sqrt148)=-0.47`

`theta=117.9`º