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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a
2:3
b
1: 3
c
1:2
d
3:2
answer is A.
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Detailed Solution
Case 1 : (2P)2=P2+Q2+2PQcosθCase 2 :(P)2=P2+Q2+2PQcos180-θAdding them5P2=2P2+2Q2 or 3P2=2Q2PQ=23