Let \( \vec{a}=\hat{i}+\hat{j}-\hat{k},\ \vec{b} \) and \( \vec{c}=\hat{j}-\hat{k} \) be three vectors such that \( \vec{a}\times\vec{b}=\vec{c} \) and \( \vec{a}\cdot\vec{b}=1 \). If the length of projection vector of the vector \( \vec{b} \) on the vector \( \vec{a}\times\vec{c} \) is \( l \) then the value of \( 3l^{2} \) is equal to ________.
