If two points \( \mathrm{P} \) and \( \mathrm{Q} \) are one the cur...

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If two points \( \mathrm{P} \) and \( \mathrm{Q} \) are one the curve \( \mathrm{y}=2^{\mathrm{x}+2} \),
\( \mathrm{P} \) such that \( \overrightarrow{\mathrm{OP}} \cdot \hat{\imath}=-1 \) and \( \overrightarrow{\mathrm{OQ}} \cdot \mathrm{i}=2 \), where \( \hat{\mathrm{i}} \) is a

W unit vector along the x-axis, then \( |\overrightarrow{\mathrm{OQ}}-4 \overrightarrow{\mathrm{OP}}| \) is equal to
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