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The resultant of vector P and vector Q if vector Q is doubled R doubled when Q is reversed R is again doubled find p:Q:R

The resultant of vector P and vector Q if vector Q is doubled R doubled when Q is reversed R is again doubled find p:Q:R

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1 Answers

Arun
25763 Points
3 years ago
R^2 = P^2 + Q^2 + 2PQ cosθ ... ( 1 ) 
4R^2 = P^2 + 4Q^2 + 4PQ cosθ ... ( 2 ) 
4R^2 = P^2 + Q^2 - 2PQ cosθ ... ( 3 ) 

Multiplying eqn. ( 1 ) by 2 and subtracting from eqn. ( 2 ), 
2R^2 = 2Q^2 - P^2 ... ( 4 ) 
Adding eqns. ( 1 ) and ( 3 ), 
5R^2 = 2Q^2 + 2P^2 ... ( 5 ) 
Subtracting eqn. ( 4 ) from eqn. ( 5 ), 
3R^2 = 3P^2 => P^2 = R^2 
Plugging R^2 = P^2 in eqn. ( 4 ), 
2P^2 = 2Q^2 - P^2 
=> Q^2 = (3/2)P^2 
=> P^2 : Q^2 : R^2 = P^2 : (3/2)P^2 : P^2 
=> P : Q : R = √2 : √3 : √2.

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