Two forces with equal magnitudes F act on

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Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $F/3$. The angle between the two forces is

A

${\cos ^{ - 1}}\left( { - \frac{{17}}{{18}}} \right)$

B

${\cos ^{ - 1}}\left( { - \frac{1}{3}} \right)$

C

${\cos ^{ - 1}}\left( {\frac{2}{3}} \right)$

D

${\cos ^{ - 1}}\left( {\frac{8}{9}} \right)$

Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $F/3$. The angle between the two forces is

$F_{_{net}}^2 = F_1^2 + F_2^2 + 2{F_1}{F_2}\cos \theta $

$⇒$ ${\left( {\frac{F}{3}} \right)^2}$$ = {F^2} + {F^2} + 2{F^2}\cos \theta $

 $⇒$ $\cos \theta = \left( { - \frac{{17}}{{18}}} \right)$