Vector Algebra

\(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\), then unit vector parallel to \(\mathbf{a}+\mathbf{b}-\mathbf{c}\) but in opposite direction is