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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 : 2

b

2 : 1

c

1 : 1

d

1: 3

answer is B.

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Detailed Solution

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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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