When two vectors of magnitudes \( P \) and \( Q \) are inclined at an angle \( \theta \), the ma...

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When two vectors of magnitudes \( P \) and \( Q \) are inclined at an angle \( \theta \), the magnitude of their resultant \( 2 P \). When the inclination is changed to \( 180-\theta \), the magnitude of the resultant is halved. Find the ratio of \( P \) to \( Q \).
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