Vector Algebra

If \(\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}\) are coplanar, then \(\lambda\) is the root of the equation