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MHT CET202410 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 cosec is

Options

  1. A3 3 2
  2. B2 2 3
  3. C2 3
  4. D3 2 2

Correct answer

D. 3 2 2

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

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