Question

Question #f066d

Answer 1

`theta=cos^-1(-17/18)`

Explanation:

let the force vectors be `F_1=F` and `F_2=F`
and the angle between them be `theta`
According to the question the resultant force is `F'=F/3`

using the parallelogram law of vector addition
`F'=sqrt(F_1^2+F_2^2+2F_1.F_2costheta`
where `theta` is the angle between the two vectors
putting the values

`F/3=sqrt(F^2+F^2+2F.Fcostheta)`
squaring on both side
`F^2/9=2F^2+2F^2costheta`

cancel the `F^2`
`=> 1/9=2+2costheta`
`=> 2costheta=1/9-2=(1-18)/9=-17/9`
`=> costheta=-17/18`
`=> theta=cos^-1(-17/18)`