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        The resultant of vector P and vector q is R if vector q doubled when q is reversed r is again doubled find p:q:r
7 months ago

Answers : (1)

Arun
12289 Points
							
Dear student
 
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.
 
 
Regards
Arun (askIITians forum exper
7 months ago
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