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JEE Main2017MathematicsVector AlgebraActual

If the vector b → = 3 j ^ + 4 k ^ is written as the sum of a vector b 1 → , parallel to a → = i ^ + j ^ and a vector b → 2 , perpendicular to a → , then b → 1 × b → 2 is equal to :

Options

  1. A6 i ^ - 6 j ^ + 9 2 k ^
  2. B- 3 i ^ + 3 j ^ - 9 k ^
  3. C- 6 i ^ + 6 j ^ - 9 2 k ^
  4. D3 i ^ - 3 j ^ + 9 k ^

Correct answer

A. 6 i ^ - 6 j ^ + 9 2 k ^

Step-by-step solution

b → 1 = b → ⋅ a → a ^ 2 = 3 j ^ + 4 k ^ ⋅ i ^ + j ^ 2 i ^ + j ^ 2 = 3 i ^ + j ^ 2 × 2 = 3 i ^ + j ^ 2 b → 1 + b → 2 = b → b → 2 = b → - b → 1 = 3 j ^ + 4 k ^ - 3 2 i ^ + j ^ b → 2 = - 3 2 i ^ + 3 2 j ^ + 4 k ^ b → 1 × b → 2 = i ^ j ^ k ^ 3 2 3 2 0 - 3 2 3 2 4 ⇒ i ^ 6 - j ^ 6 + k ^ 9 4 + 9 4 = 6 i ^ - 6 j ^ + 9 2 k ^

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