The set of value of x for which the angle between the $\vec{a}=2 x^2 \hat{i}+4 x \hat{j}+\hat{k}$ and $\vec{b}=7 \hat{i}-2 \hat{j}+x \hat{k}$ is obtuse is:

$\left(0, \frac{1}{2}\right)$ $\left(0, \frac{1}{3}\right)$ $\left(\frac{1}{2}, \frac{1}{3}\right)$ $(0,1)$

$\left(0, \frac{1}{2}\right)$

The correct answer is Option (1) - $\left(0, \frac{1}{2}\right)$