A st. line is drawn through the point \( \mathrm{P}(\sqrt{3}, 2) \) making an angle of \( \frac{...

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A st. line is drawn through the point \( \mathrm{P}(\sqrt{3}, 2) \) making an angle of \( \frac{\pi}{6} \) with positive direction of the \( x \)-axis. If it meets the st. line \( \sqrt{3} x-4 y+8=0 \) in \( \mathrm{Q} \). find the length of \( |\mathrm{PQ}| \).
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