Question

What is the angle between `<6,-2,2 >` and `< -2, 7 ,-2 >`?

Answer 1

The angle is `126.8º`

Explanation:

The angle is given by the dot product definition

`vecu.vecv=∥vecu∥*∥vecv∥*costheta`

Here, `vecu=〈6,-2,2〉`

and `vecv=〈-2,7,-2〉`

The dot product is

`vecu.vecv=〈6,-2,2〉.〈-2,7,-2〉=(-12-14-4)=-30`

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

The modulus of `vecv=∥〈-2,7,-2〉∥=sqrt(4+49+4)=sqrt57`

Then,

`costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)=-30/(sqrt44sqrt57)=-0.6`

and `theta=126.8º`