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BITSAT2019MathematicsVector AlgebraActual

If a → = i ^ + 2 j ^ + 3 k ^ , b → = - i ^ + 2 j ^ + k ^ , c → = 3 i ^ + j ^ and a → + p b → is normal to c → , then p is equal to

Options

  1. A0
  2. B1
  3. C5
  4. D3

Correct answer

C. 5

Step-by-step solution

a → + p b → is normal to c → ∴   a → + p b → · c → = 0 1 - p i ^ + 2 + 2 p j ^ + 3 + p k ^ · 3 i ^ + j ^ = 0 3 - 3 p + 2 + 2 p = 0 ⇒ p = 5

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