Question

What is the angle between `<-4,8,0>` and `< -3,6,-2>`?

Answer 1

`(vecu,vecv)=0.29 rad`

Explanation:

Let `vecu=(-4,8,0)`
and `vecv=(-3,6-2)`
Use the dot product definition, `vecu*vecv=∣vecu∣*∣vecv∣*cos(vecu,vecv)`
`vecu.vecv=12+48+0=60`
`∣∣vecu∣∣= sqrt(16+64+0)=sqrt80`
`∣∣vecv∣∣=sqrt(9+36+4)=sqrt49=7`
So `cos(vecu,vecv)=(vecu.vecv)/(∣vecu∣∣vecv∣)=60/(sqrt80*7)`
`(vecu,vecv)=arccos(60/(7sqrt(80)) )=0.29rad`