Vector Algebra

For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying

\(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9 \text { and }|2 \vec{a}+k \vec{b}+k \vec{c}|=3 \text {, }\)

the positive value of k is :