Vector Algebra

If \(\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{c}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}\) is perpendicular to \(\overline{\mathrm{c}}\), then \(\lambda=\)