Let \( S \) be the set of all \( a \in \mathbb{R} \) for which the angle between the vectors \( \vec{u} = a(\log_{e} b)\hat{\imath} - 6\hat{\jmath} + 3\hat{k} \) and \( \vec{v} = (\log_{e} b)\hat{\imath} + 2\hat{\jmath} + 2a(\log_{e} b)\hat{k}, \ (b>1) \) is acute. Then \( S \) is equal to:
