Let a = i +2 j + k and b =2 i + j - k. Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a. Then such a vector c is:

Let $\displaystyle \vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\displaystyle \vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Let $\displaystyle \hat{c}$ be a unit vector in the plane of the vectors $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ and be perpendicular to $\displaystyle \vec{a}$. Then such a vector $\displaystyle \hat{c}$ is :