Let the vectors u_1= i + j +a k, u_2= i +b j + k and u_3=c i + j + k be coplanar. If the vectors v_1=(a+b) i +c j +c k, v_2=a i +(b+c) j +a k and…

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