The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then, P2:Q2:R2 given by
A
2:2:3
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B
3:2:2
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C
2:3:2
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D
2:3:1
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Solution
The correct option is C2:3:2 Given, R=P+Q |R|2=|P|2+|Q|2+2|P||Q|cosθ...(1) Now 2R=P+2Q 4|R|2=|P|2+4|Q|2+4|P||Q|cosθ...(2) Now 2R=P−Q 4|R|2=|P|2+|Q|2−2|P||Q|cosθ...(3) Add (1) and (3) 5|R|2=2|P|2+2|Q|2...(4) Now multiply equation (3) with 2 and then add it with (2) 12|R|2=3|P|2+6|Q|2 ⇒4|R|2=|P|2+2|Q|2...(5) Now equation (4)-(5) |R|2=|P|2 Now from equation (4) 5|R|2=2|R|2+2|Q|2 ⇒|Q|2=32|R|2 Therefore, |P|2:|Q|2:|R|2=|R|2:32|R|2:|R|2 =2:3:2