The resultant of P⃗ and Q⃗ is perpendicular to P⃗. The magnitude P is then doubled without changing its direction, and the new resultant becomes perpendicular to Q⃗. Find Q/P, where P is the original magnitude.
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Question

The resultant of P⃗ and Q⃗ is perpendicular to P⃗. The magnitude P is then doubled without changing its direction, and the new resultant becomes perpendicular to Q⃗. Find Q/P, where P is the original magnitude.

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G1 Physics · Accepted Answer

Initially P+Q cosθ=0. After doubling P, Q+2P cosθ=0. Eliminating cosθ gives Q²=2P², hence Q/P=√2.