Vector Algebra

Let \(\mathbf{a}=2 \mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=\mathbf{i}+2 \mathbf{j}-\mathbf{k}\) and \(a\) unit vector \(\mathbf{c}\) be coplanar. If \(\mathbf{c}\) is perpendicular to \(\mathbf{a}\), then c equals to