Let a vector \( \vec{a} \) be coplanar with vectors \( \vec{b}=2 \hat{i}+\hat{j}+\hat{k} \) and \( \vec{c}=\hat{i}-\hat{…

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: