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)#