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JEE Main202117 Mar 2021Morning ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ - 3 j ^ + 4 k ^ and b → = 7 i ^ + j ^ - 6 k ^ If r → × a → = r → × b → , r → · ( i ^ + 2 j ^ + k ^ ) = - 3 , then r → · ( 2 i ^ - 3 j ^ + k ^ ) is equal to:

Options

  1. A12
  2. B8
  3. C13
  4. D10

Correct answer

A. 12

Step-by-step solution

r → × a → - r → × b → = 0 ⇒ r → × a → - b → = 0 ⇒ r → = λ a → - b → ⇒ r → = λ - 5 i ^ - 4 j ^ + 10 k ^ Also r → · i ^ + 2 j ^ + k ^ = - 3 ⇒ λ - 5 - 8 + 10 = - 3 λ = 1 Now r → = - 5 i ^ - 4 j ^ + 10 k ^ = r → · 2 i ^ - 3 j ^ + k ^ = - 10 + 12 + 10 = 12

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