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MHT CET202416 May 2024Evening ShiftMathematicsVector AlgebraActual

If a , b , c are three vectors such that a 0 and a b =2 a c ,| a |=| c |=1,| ~b |=4 and | b c |= 15 . If b -2 c = a , then is

Options

  1. A1
  2. B-4
  3. C3
  4. D-2

Correct answer

B. -4

Step-by-step solution

If angle between b and c is and aligned & | b c |= 15 & | ~b || c | = 15 & (4)(1) = 15 & = 15 4 & = 1 4 aligned aligned & Now, b -2 c = a & | b -2 c |^2= ^2| a |^2 & | ~b |^2+4| c |^2-4 ~b c = ^2| a |^2 & 16+4-4(| ~b | a )= ^2 & 20-4 (4 1 1 4 )= ^2 & 16= ^2 & = 4 aligned

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