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JEE Main202116 Mar 2021Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ + 2 j ^ - 3 k ^ and b → = 2 i ^ - 3 j ^ + 5 k ^ . If r → × a → = b → × r → , r → · α i ^ + 2 j ^ + k ^ = 3 and r → · ( 2 i ^ + 5 j ^ - α k ^ ) = - 1 , α ∈ R , then the value of α + | r → | 2 is equal to :

Options

  1. A9
  2. B15
  3. C13
  4. D11

Correct answer

B. 15

Step-by-step solution

r → × a → = b → × r → ⇒ r → × a → + b → = 0 r → = λ → a → + b → ⇒ r → = λ → i ^ + 2 j ^ - 3 k ^ + 2 i ^ - 3 j ^ + 5 k ^ r → = λ → 3 i ^ - j ^ + 2 k ^     . . . 1 r → · ( α i ^ + 2 j ^ + k ^ ) = 3 Put r → from 1 α λ = 1     . . . 2 r → · 2 i ^ + 5 j ^ - α k ^ = - 1 Put r → from (1) 2 λ α - λ = 1 &#1

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