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

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Correct option is A

Case 1 : (2P)2=P2+Q2+2PQcos⁡θCase 2 :(P)2=P2+Q2+2PQcos⁡180-θAdding them5P2=2P2+2Q2 or 3P2=2Q2PQ=23

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

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Ready to Test Your Skills?

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