Question

What is the angle between `<-1,-2,8 >` and `<-2,6,-4>`?

Answer 1

THe angle is `126.9º`

Explanation:

The angle is obtained by using the definition of the dot product
`vecu.vecv=∣vecu∣*∣vecv∣costheta`
where `theta` is the angle between the vectors `(vecu,vecv)`

So `costheta=(vecu.vecv)/(∣vecu∣*∣vecv∣)`

Here `vecu=〈-1,-2,8〉`

and `vecv=〈-2,6,-4〉`

The dot product is given by `vecu.vecv=〈u_1,u_2,u_3〉〈v_1,v_2,v_3〉=u_1v_1+u_2v_2+u_3v_3`
So `vecu.vecv=2-6-32=-36`

`∣vecu∣=sqrt(u_1^2+u_2^2+u_3^2)=sqrt(1+4+64)=sqrt69`

`∣vecv∣=sqrt(v_1^2+v_2^2+v_3^2)=sqrt(4+36+16)=sqrt56`

So `costheta=-36/(sqrt69.sqrt56)=-0.601`
`theta=126.9º`