What is the angle between two forces of equal magnitude, $F_a$ and $F_b$ , when the magnitude of their resultant is also equal to the magnitude of either of these forces?

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Answer 1 · 2016-07-28T13:13:20

$theta=(2pi)/3$

Let the angle between $F_a and F_b$ be $theta$ and their resultant is $F_r$ So

$F_r^2=F_a^2+F_b^2+2F_aF_bcostheta$
Now by the given condition
let $F_a=F_b=F_r=F$

So

$F^2=F^2+F^2+2F^2costheta$

$=>costheta=-1/2=cos(2pi/3)$

$:.theta=(2pi)/3$

What is the angle between two forces of equal magnitude, F_aF_a and F_bF_b, when the magnitude of their resultant is also equal to the magnitude of either of these forces?