Vector Algebra

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