Vector Algebra

Let \(\bar{a}=\hat{i}+2 \hat{j}-\hat{k}\) and \(\bar{b}=\hat{i}+\hat{j}-\hat{k}\) be two vectors. If \(\bar{c}\) is a vector such that \(\bar{b} \times \bar{c}=\bar{b} \times \bar{a}\) and \(\overline{\mathrm{c}} \cdot \overline{\mathrm{a}}=0\), then \(\overline{\mathrm{c}} \cdot \overline{\mathrm{b}}\) is