The value of $x$ for which the angle between $\vec{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k}$ and $\vec{b} = 7\hat{i} - 2\hat{j} + \hat{k}$ is obtuse and the angle between $\vec{b}$ and the z-axis is acute and less than $\frac{\pi}{6}$ is: