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JEE Main2004MathematicsVector AlgebraActual

Let a , b and c be non-zero vectors such that ( a b ) c = 1 3 | b || c | a . If is the acute angle between the vectors b and c , then equals

Options

  1. A1 3
  2. B2 3
  3. C2 3
  4. D2 2 3

Correct answer

D. 2 2 3

Step-by-step solution

( a b ) c = 1 3 | b || c | a ( a c ) b -( b c ) a = 1 3 | b || c | a ( a c ) b = ( 1 3 | b || c |+( b c ) ) a a c =0 and 1 3 | b || c |+( b c )=0 | b || c | ( 1 3 + )=0 =-1 / 3 = 2 2 3

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