Question
Two equal forces have their resultant equal to either. What is the inclination between them?
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Answer
Here, A = F; B = F, R = F$\text{R}=\sqrt{\text{A}^2+\text{B}^2+2\text{AB}\cos\theta}$
$\text{F}=\sqrt{\text{F}^2+\text{F}^2+2\text{F}.\text{F}\cos\theta}$
$\text{F}=\text{F}\sqrt{2(1+\cos\theta)}$
$1=2(1+\cos\theta)$
$\cos\theta=-\frac{1}{2}=\cos120^\circ$
$\theta=120^\circ$
$\text{F}=\sqrt{\text{F}^2+\text{F}^2+2\text{F}.\text{F}\cos\theta}$
$\text{F}=\text{F}\sqrt{2(1+\cos\theta)}$
$1=2(1+\cos\theta)$
$\cos\theta=-\frac{1}{2}=\cos120^\circ$
$\theta=120^\circ$
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