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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

If a , b , c are three independent vectors and there exists a non zero scalar traid (l, m, n) such that l(3 a +2 b + c )+m(2 a +2 b +3 c )+n( a +2 b +5 c )= 0 , then

Options

  1. Al=m=n
  2. Bl=n
  3. Cl=n, m+2 n=0
  4. Dm+2 n=0,1+n=0

Correct answer

C. l=n, m+2 n=0

Step-by-step solution

Given, l(3 a +2 b + c )+m(2 a +2 b +3 c )+n( a +2 b +5 c )=0 Where l, m, n are scalar a (3 l+2 m+n)+2 b (l+m+n)+ c (l+3 m+5 n)=0 a , b , c are independent vector From Eqs. (ii) and (iii), m+2 n=0 Putting the value of m in Eq. (i), we get aligned & 3 l+2(-2 n)+n =0 3 l-3 n=0 l=n l & =n, m+2 n =0 aligned

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