Let S be the set of all a ∈ R for which the angle between the vectors u =a( log_e b) i -6 j +3 k and v =( log_e b) i +2 j +2 a( log_e b) k,(b>1) is…

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