Let a =α i + j - k and b =2 i + j -α k, α>0. If the projection of a × b on the vector - i +2 j -2 k is 30, then α is equal to:

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