# Two equal vectors have a resultant equal to either. At what angle are they inclined to each other?

## OR: Under what condition will the sum of two vectors of equal magnitude have magnitude equal to either vector?

Let the two vectors be $\overrightarrow{P}$ and $\overrightarrow{Q}$ and let $R$ be their resultant. If $\theta$ is the angle between the two vectors, then,

$R=\sqrt{P^2+Q^2+2PQ\cos\theta}$

According to the question, $R=P=Q$.

$\therefore R=\sqrt{R^2+R^2+2R^2\cos\theta}$ $R=R\sqrt{2+2\cos\theta}$ $1=2(1+\cos\theta)$ $\frac{1}{2}=1+\cos\theta$ $\cos\theta=-\frac{1}{2}$ $\therefore\theta=120°$

Hence, the angle between the two vectors should be $120°$.