Two l vectors having equal magnitude , have a resultant equal to either of the two. The angle between them is

Let two vectors are A and B, inclined at an angle $\mathbf{\theta }$.

Resultant of the two vectors A and B,

$\left|\mathbf{R}\right|=\sqrt{|\mathbf{A}{|}^2+|\mathbf{B}{|}^2+2\left|\mathbf{A}\right|\left|\mathbf{B}\right|\cos \theta }$

Let $\left|\mathbf{A}\right|=\left|\mathbf{B}\right|=a$

According to the question, $\left|\mathbf{R}\right| = a$
From Eq. (i), we get

$a=\sqrt{a^2+a^2+2aa\cos \theta }$

$\Rightarrow a^2=a^2+a^2+2a^2\cos \theta$

$\Rightarrow 2a^2\cos \theta =-a^2$

$\Rightarrow \cos \theta =-1/2$

$\Rightarrow \theta =120°$