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# If the angle $\theta$ between the vectors $\overrightarrow {a}=2x^2 \overrightarrow {i}+ 4x \overrightarrow {j}+ \overrightarrow {k}$ and $\overrightarrow {b}=7 \overrightarrow{i}-2 \overrightarrow {j}+x \overrightarrow {k}$ is such that $90^{\circ} < \theta <180^{\circ}$ then $x$ lies in the interval ::

$\begin {array} {1 1} (1)\;\bigg(0,\frac{1}{2}\bigg) & \quad (2)\;\bigg(\frac{1}{2},1\bigg) \\ (3)\;\bigg(1,\frac{3}{2}\bigg) & \quad (4)\;\bigg(\frac{1}{2},\frac{3}{2}\bigg) \end {array}$

$(1)\;\bigg(0,\frac{1}{2}\bigg)$