Vector Algebra

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