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 :