Let the vectors \( \vec{u}_{1} = \hat{i} + \hat{j} + a\hat{k} \), \( \vec{u}_{2} = \hat{i} + b\hat{j} + \hat{k} \) and \( \vec{u}_{3} = c\hat{i} + \hat{j} + \hat{k} \) be coplanar. If the vectors \( \vec{v}_{1} = (a+b)\hat{i} + c\hat{j} + c\hat{k} \), \( \vec{v}_{2} = a\hat{i} + (b+c)\hat{j} + a\hat{k} \) and \( \vec{v}_{3} = b\hat{i} + b\hat{j} + (c+a){k} \) are also coplanar, then \( 6(a+b+c) \) is equal to:
