Vector Algebra

If \(\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(\overline{\mathrm{c}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}\) are such that \(\bar{a}+\lambda \bar{b}\) is perpendicular to \(\bar{c}\), then the value of \(\lambda\) is