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JEE Main202227 Jul 2022Morning ShiftMathematicsVector AlgebraActual

Let a → = α i ^ + j ^ + β k ^ and b → = 3 i ^ - 5 j ^ + 4 k ^ be two vectors, such that a → × b → = - i ^ + 9 i ^ + 12 k ^ . Then the projection of b → - 2 a → on b → + a → is equal to

Options

  1. A2
  2. B39 5
  3. C9
  4. D46 5

Correct answer

D. 46 5

Step-by-step solution

Let a → = α i ^ + j ^ + β k ^ , b → = 3 i ^ - 5 j ^ + 4 k ^ Now finding a → × b → = - i ^ + 9 j ^ + 12 k ^ = i ^ j ^ k ^ α 1 β 3 - 5 4 ⇒   4 + 5 β i ^ + 3 β - 4 α j ^ + - 5 α - 3 k ^ = - i ^ + 9 j ^ + 12 k ^ Now on comparing side we get,   4 + 5 β = - 1 , 3 β - 4 α = 9 , - 5 α - 3 = 12 β = - 1 ,    α = - 3 So, a → = - 3 i ^ + j ^ - k ^   &   b → = 3 i ^ - 5 j ^ + 4 k

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