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