The value of $\alpha$ if the angle between $\vec{p}=2\alpha^2\hat{i}-3\alpha\hat{j}+\hat{k}$ and $\vec{q}=\hat{i}+\hat{j}+\alpha\hat{k}$ is obtuse, is

$(0, 1)$

The correct answer is Option (2) → $(0, 1)$ ##

For obtuse angle, $\cos \theta < 0 \Rightarrow \vec{p} \cdot \vec{q} < 0$

$2\alpha^2 - 3\alpha + \alpha < 0 \Rightarrow 2\alpha^2 - 2\alpha < 0 \Rightarrow \alpha \in (0, 1)$