Given that the magnitude of each of the two vectors $\overrightarrow{\mathit{a}}$ and $\overrightarrow{\mathit{b}}$ have same magnitude.
⇒ $\left|\overrightarrow{\mathit{a}}\right|$ = $\left|\overrightarrow{\mathit{b}}\right|$ ... (i)
the angle between $\overrightarrow{\mathit{a}}$ and $\overrightarrow{\mathit{b}}$ is 60°
⇒ θ = 60°
and $\overrightarrow{\mathit{a}}$ . $\overrightarrow{\mathit{b}}$ = $\frac{3}{2}$ ... (iii)
Since,
$\overrightarrow{\mathit{a}}$ . $\overrightarrow{\mathit{b}}$ = $\left|\overrightarrow{\mathit{a}}\right|$ $\left|\overrightarrow{\mathit{b}}\right|$ cos θ
⇒ $\left|\overrightarrow{\mathit{a}}\right|$ $\left|\overrightarrow{\mathit{a}}\right|$ cos 60° = $\frac{9}{2}$ From (i),(ii) and (iii)
⇒ ${\left|\overrightarrow{\mathit{a}}\right|}^2$ × $\frac{1}{2}$ = $\frac{9}{2}$
⇒ ${\left|\overrightarrow{\mathit{a}}\right|}^2$ = 9
⇒ $\left|\overrightarrow{\mathit{a}}\right|$ = 3
⇒ $\left|\overrightarrow{\mathit{a}}\right|$ = $\left|\overrightarrow{\mathit{b}}\right|$ = 3 ... From (i)