List of practice Questions

If the three vectors \( \vec{a} = \hat{i} + \lambda\hat{j} + \hat{k} \), \( \vec{b} = \hat{j} + \hat{k} \), and \( \vec{c} = \hat{i} + \hat{j} \) are coplanar, find the exact value of the scalar constant \( \lambda \).