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MHT CET202310 May 2023Morning ShiftMathematicsVector AlgebraActual

Let a , b , 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 the value of is

Options

  1. A2 2 3
  2. B- 2 3
  3. C2 3
  4. D2 3

Correct answer

A. 2 2 3

Step-by-step solution

Given: ( a b ) c = 1 3 | b || c |⁻ 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 & ^2 = 8 9 & = 8 9 = 2 2 3 aligned

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