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