Question

Two equal forces $\overrightarrow{F}$ are acting such that the magnitude of their resultant is equal to F. They must be inclined at an angle of __ degrees

Answer 1

Here $|\overrightarrow{A}|=F;|\overrightarrow{B}|=Fand|\overrightarrow{R}|=F;\theta =?$

Using the direct formula,

$R=\sqrt{A^2+B^2+2ABcos\theta }F=\sqrt{F^2+F^2+2F^{2}cos\theta }F=F\sqrt{2(1+cos\theta )}cos\theta =-\frac{1}{2}\theta ={120}^{\circ }$

In case you are wondering how that formula came –It’s the parallelogram law of vectors addition.