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