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

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