Question #f066d

1 Answer
Jan 31, 2018

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)