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:

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

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

if angle → obtuse

$\vec a.\vec b<0$

$⇒14x^2-8x+x=0$

so $14x^2=7x$

so $x=0,\frac{1}{2}$