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JEE Main20236 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ + 3 j ^ + 4 k ^ , b → = i ^ - 2 j ^ - 2 k ^ and c → = - i ^ + 4 j ^ + 3 k ^ . If d → is a vector perpendicular to both b → and c → , and a → · d → = 18 , then | a → × d → | 2 is equal to

Options

  1. A640
  2. B680
  3. C720
  4. D760

Correct answer

C. 720

Step-by-step solution

Given that, a → = 2 i ^ + 3 j ^ + 4 k ^ ,   b → = i ^ - 2 j ^ - 2 k ^ and c → = - i ^ + 4 j ^ + 3 k ^ . Let us find b → × c → ⇒ b → × c → = i ^ j ^ k ^ 1 - 2 - 2 - 1 4 3 = - 6 + 8 i ^ - 3 - 2 j ^ + 4 - 2 k ^ ⇒ b → × c → = 2 i ^ - j ^ + 2 k ^ Since d → is perpendicular to both b →   and   c → ∴ d → = λ ( 2 i ^ - j ^ + 2 k ^ ) Also a → · d → = 18 ⇒ λ 2 i ^ + 3

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