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JEE Main2018MathematicsVector AlgebraActual

Let a → = i ^ + j ^ + k ^ , c → = j ^ - k ^ and a vector b → be such that a → × b → = c → and a → ⋅ b → = 3 . Then b → equals

Options

  1. A11 3
  2. B11 3
  3. C11 3
  4. D11 3

Correct answer

C. 11 3

Step-by-step solution

Given, a → × b → = c → ⇒ a → × a → × b → = a → × c → ⇒ a → ⋅ b → a → - a → ⋅ a → b → = a → × c → a → × c → = i ^ j ^ k ^ 1 1 1 0 1 - 1 = - 2 i ^ + j ^ + k ^ ⇒ 3 a → - 3 b → = - 2 i ^ + j ^ + k ^ ⇒ 3 i ^ + 3 j ^ + 3 k ^ - 3 b → = - 2   i ^ + j ^ + k ^ ⇒ b → = 1 3 5 i ^ + 2 j ^ + 2 k ^ ∴  b → =

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