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Q.

P,Q,R,S are vector of equal magnitude. If  P + Q - R = 0 angle between  P and  Q is   θ1 . If  P + Q - S = 0 angle between  P and  S is θ2. The ratio of θ1 to θ2 is

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a

1: 3

b

2 : 1 

c

1 : 2

d

1 : 1

answer is B.

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Detailed Solution

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P+Q=R;P+Q=S,

tan θ2=Qsinθ1P+Qcosθ1  tan θ2=sin θ11+cosθ1 sin θ2cos θ2=sin θ11+cos θ1 sin θ2= sin(θ1-θ2) θ2=θ1-θ2  θ2=θ12  

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