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JEE Main202131 Aug 2021Evening ShiftMathematicsVector AlgebraActual

Let a → , b → , c → be three vectors mutually perpendicular to each other and have same magnitude. If a vector r → satisfies a → × r → - b → × a → + b → × r → - c → × b → + c → × r → - a → × c → = 0 → , then r → is equal to:

Options

  1. A1 3 ( a → + b → + c → )
  2. B1 3 ( 2 a → + b → - c → )
  3. C1 2 ( a → + b → + c → )
  4. D1 2 ( a → + b → + 2 c → )

Correct answer

C. 1 2 ( a → + b → + c → )

Step-by-step solution

Given: a → × r → - b → × a → + b → × r → - c → × b → + c → × r → - a → × c → = 0 → ⇒ ( a → . a → ) ( r → - b → ) - ( a → · ( r → - b → ) ) a → + ( b → · b → ) ( r → - c → ) - ( b → · ( r → - c → ) ) b → + ( c → . c → ) ( r → - a → ) - ( c → . ( r → - a &#8594

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