Vector Algebra

A vector which is orthogonal to the vector $\bar{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and coplanar with the vectors $\bar{b} = 3\hat{i} + 2\hat{j}$ and $\bar{c} = 2\hat{i} + \hat{j} + 3\hat{k}$ is