Let $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}$ and $\bar{c}=\hat{j}-\hat{k}$ be three vectors such that $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\overline{\mathrm{c}}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=1$. If the length of projection vector of the vector $\overline{\mathrm{b}}$ on the vector $\overline{\mathrm{a}} \times \overline{\mathrm{c}}$ is $l$, then the value of $3 l^2$ is