Let \( \vec{a}=\alpha \hat{i}+\hat{j}+\beta \hat{k} \) and \( \vec{b}=3\hat{i}-5\hat{j}+4\hat{k} \) be two vectors, suthat \( \vec{a}\times \vec{b}=-\hat{i}+9\hat{j}+12\hat{k} \). Then the projection of \( \vec{b}-2\vec{a} \) on \( \vec{b}+\vec{a} \) is equal to:
