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MHT CET202416 May 2024Morning ShiftMathematicsVector AlgebraActual

Let a , b and c be three non-zero vectors such that no two of them are collinear and .( a b ) c = 1 3 | ~b | c , a . If is the angle between vectors b and c , then the value of is

Options

  1. A2 3
  2. B-2 2 3
  3. C2 2 3
  4. D- 2 3

Correct answer

C. 2 2 3

Step-by-step solution

Given, ( a b ) c = 1 3 | ~b || c | a We know that, ( a b ) c =( a c ) b -( b c ) a On comparing, we get aligned & 1 3 | ~b || c |=- b c & 1 3 | ~b || c |=-| b || c | & = -1 3 & ^2 = 1 9 aligned aligned ^2 & =1- ^2 & =1- 1 9 ^2 & = 8 9 & = 8 9 = 2 2 3 aligned

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