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JEE Main202310 Apr 2023Evening ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ + 7 j ^ - k ^ , b ^ = 3 i ^ + 5 k ^ and c → = i ^ - j ^ + 2 k ^ Let d → be a vector which is perpendicular to both a → and b → , and c → · d → = 12 . Then - i ^ + j ^ - k ^ · c → × d → is equal to

Options

  1. A24
  2. B44
  3. C42
  4. D48

Correct answer

B. 44

Step-by-step solution

Given, a → = 2 i ^ + 7 j ^ - k ^ ,   b ^ = 3 i ^ + 5 k ^ and c → = i ^ - j ^ + 2 k ^ And d → be a vector which is perpendicular to both a → and b → , So, d → = λ a → × b → Now finding, a → × b → = i ^ j ^ k ^ 2 7 - 1 3 0 5 ⇒ a → × b → = 35 i ^ - 13 j ^ - 21 k ^ So, d → = λ 35 i ^ - 13 j ^ - 21 k ^ Also given, c → · d → = 12 ⇒ c → · d → = i ^ - j ^ + 2 k ^ · &

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