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