If a is a nonzero vector such that its projections on the vectors 2 i - j +2 k, i +2 j -2 k and k are equal, then a unit vector along a is:

If $\displaystyle \overrightarrow{\mathrm{a}}$ is a nonzero vector such that its projections on the vectors $\displaystyle 2 \hat{i}-\hat{j}+2 \hat{k}, \hat{i}+2 \hat{j}-2 \hat{k}$ and $\displaystyle \hat{k}$ are equal, then a unit vector along $\displaystyle \overrightarrow{\mathrm{a}}$ is :