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