Let the vectors $\overrightarrow{\mathrm{u}}_1=\hat{\mathrm{i}}+\hat{\mathrm{j}}+a \hat{\mathrm{k}}, \overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+b \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{u}}_3=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ be coplanar. If the vectors $\vec{v}_1=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \quad \vec{v}_2=a \hat{i}+(b+c) \hat{j}+a \hat{k}$ and $\vec{v}_3=b \hat{i}+b \hat{j}+(c+a) \hat{k}$ are also coplanar, then $6(a+b+$ equal to