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JEE Main202127 Jul 2021Morning ShiftMathematicsVector AlgebraActual

Let a → = i ^ + j ^ + 2 k ^ and b → = - i ^ + 2 j ^ + 3 k ^ . Then the vector product a → + b → × a → × a → - b → × b → × b → is equal to :

Options

  1. A5 34 i ^ - 5 j ^ + 3 k ^
  2. B7 34 i ^ - 5 j ^ + 3 k ^
  3. C7 30 i ^ - 5 j ^ + 7 k ^
  4. D5 30 i ^ - 5 j ^ + 7 k ^

Correct answer

B. 7 34 i ^ - 5 j ^ + 3 k ^

Step-by-step solution

a → = i ^ + j ^ + 2 k ^ b → = - i ^ + 2 j ^ + 3 k ^ a → + b → = 3 j ^ + 5 k ^ ; a → · b → = - 1 + 2 + 6 = 7 Now a → × a → - b → × b → × b → = a → × a → × b → - b → × b → × b → = a → × a → × b → - 0 × b → = a → × a → × b → × b → = a → · b → a → - a → · a → b &#

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