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Two vectors \( \vec{P} \) and \( \vec{Q} \) act at a point and have a resultant \( \overrightarrow{R_{1}} \). If \( \vec{Q} \) is replaced by the vector \( \frac{\left(R_{1}^{2}-P^{2}\right)}{Q} \), acting in the opposite direction to that of \( \vec{Q} \), show that the resultant is still of magnitude \( \overrightarrow{R_{1}} \)
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