Vector Algebra

Let \(\overrightarrow{\mathrm{a}}=\alpha \hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0\). If the projection of \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\) on the vector \(-\hat{i}+2 \hat{j}-2 \hat{k}\) is 30, then \(\alpha\) is equal to :