For three unit vectors \(\vec{a}, \vec{b}, \vec{c}\) satisfying \(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{…

For three unit vectors \(\vec{a}, \vec{b}, \vec{c}\) satisfying \(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9\) and \(|2 \vec{a}+k \vec{b}+k \vec{c}|=3\), the positive value of \(k\) is

[JEE Main 2026, 28 Jan (Shift 1)]