Question
If the vectors $\vec{a} = (c \log_{2} x) \hat{i} - 6 \hat{j} + 3 \hat{k}$ and $\vec{b} = (\log_{2} x) \hat{i} + 2 \hat{j} + (2c \log_{2} x) \hat{k}$ make an obtuse angle for any $x \in (0, \infty)$, then $c$ belongs to
If the vectors $\vec{a} = (c \log_{2} x) \hat{i} - 6 \hat{j} + 3 \hat{k}$ and $\vec{b} = (\log_{2} x) \hat{i} + 2 \hat{j} + (2c \log_{2} x) \hat{k}$ make an obtuse angle for any $x \in (0, \infty)$, then $c$ belongs to