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JEE Main202329 Jan 2023Evening ShiftMathematicsVector AlgebraActual

If a → = i ^ + 2 k ^ , b → = i ^ + j ^ + k ^ , c → = 7 i ^ - 3 j ^ + 4 k ^ , r → × b → + b → × c → = 0 → and r → · a → = 0 then r → . c → is equal to:

Options

  1. A34
  2. B12
  3. C36
  4. D30

Correct answer

A. 34

Step-by-step solution

Given, r → × b → + b → × c → = 0 → ⇒ r → × b → - c → × b → = 0 → ⇒ r → - c → × b → = 0 ⇒ r → - c → | | b → Therefore, r → - c → = λ b → ⇒ r → = c → + λ b → Also, r → · a → = 0 (given) ⇒ c → + λ b → · a → = 0 ⇒ c → · a → + λ b → · a →

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