Let a =α i + j +β k and b =3 i -5 j +4 k be two vectors, such that a × b =- i +9 i +12 k. Then the projection of b -2 a on b + a is equal to

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