Let a =3 i - j +2 k, b = a ×( i -2 k ) and c = b × k. Then the projection of c -2 j on a is:

Let $\displaystyle \overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})$ and $\displaystyle \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}$. Then the projection of $\displaystyle \overrightarrow{\mathrm{c}}-2 \hat{j}$ on $\displaystyle \vec{a}$ is :