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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Let O be the interior point of A B C such that 2 O A +3 O B +6 O C =0 where O is origin. If Area of ( A B C) Area of ( A O B) = m n , where m and n are relatively prime, then (m-n) is equal to

Correct answer

5

Step-by-step solution

Area of A B C= 1 2 | a b + b c + c a | Now given 2 a +3 b +6 c =0 Cross with a , 3 a b +6 a c =0 or a b =2( c a )....(1) Again cross with b 2 a b +6 c b =0 or a b =3( b c ) Area of OAB = 1 2 | a b | Arca of ABC Area of AOB = 1 2 | a b | (1+ 1 2 + 1 3 ) 1 2 | a b | = 11 6 So m =11 . n =6 ( m - n )=5

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