NIMCET 2020 — Mathematics PYQ

Concept:
If 2 forces are $\vec{a}$ and $\vec{b}$
Resultant of $\vec{a}$ and $\vec{b}$:
$|\vec{a}+\vec{b}|=\sqrt{a^2+b^2+2ab\cos \theta }$

Where $a$, $b$ are magnitude of vectors $\vec{a}$ and $\vec{b}$ and $\theta$ is angle between them.

Calculation:
Given:
Resultant of forces $F_1$ and $F_2$ = $|\overrightarrow{F_1}+\overrightarrow{F_2}|$
$\Rightarrow \sqrt{(F_1^2+F_2^2)}=\sqrt{F_1^2+F_2^2+2F_1{F}_2\cos \theta }$
$\Rightarrow F_1^2+F_2^2=F_1^2+F_2^2+2F_1{F}_2\cos \theta$
$\Rightarrow 0=2F_1{F}_2\cos \theta$
$\Rightarrow \cos \theta =0$
$\Rightarrow \theta =90^{\circ }$