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MHT CET202411 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 the vectors b and c , then value of is

Options

  1. A2 3
  2. B- 2 3
  3. C- 1 3
  4. D2 2 3

Correct answer

D. 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 & ^2 =1- ^2 & =1- 1 9 aligned array ll & ^2 = 8 9 & = 8 9 = 2 2 3 array

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