Let a vector \( \vec{a} \) be coplanar with vectors \( \vec{b}=2\hat{i}+\hat{j}+\hat{k} \) and \( \vec{c}=\hat{i}-\hat{j}+\hat{k} \). If \( \vec{a} \) is perpendicular to \( \vec{d}=3\hat{i}+2\hat{j}+6\hat{k} \), and \( |\vec{a}|=\sqrt{10} \). Then a possible value of \( [\vec{a}\ \vec{b}\ \vec{c}] + [\vec{a}\ \vec{b}\ \vec{d}] + [\vec{a}\ \vec{c}\ \vec{d}] \) is equal to:
