Question

What is the angle between `<-3,2,0>` and `< 5,0,2 >`?

Answer 1

`theta=cos^-1(-5/14)~~111`

Explanation:

We will use the definition of the dot product:
`vec(v_1)*vec(v_2) = |vec(v_1)||vec(v_1)|costheta`
`costheta=(vec(v_1)*vec(v_2))/(|vec(v_1)||vec(v_1)|)`
Now substituting `vec(v_1) =<-3,2,0>` and `vec(v_2)=<5,0,2>`

`costheta=(-15+0+0)/ (((-3)^2+2^2)*(5^2+2^2))= -5/14`

`theta=cos^-1(-5/14)~~111^o`