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JEE Main202122 Jul 2021Morning ShiftMathematicsVector AlgebraActual

Let a vector a → be coplanar with vectors b → = 2 i ^ + j ^ + k ^ and c → = i ^ - j ^ + k ^ . If a → is perpendicular to d → = 3 i ^ + 2 j ^ + 6 k ^ , and | a → | = 10 . Then a possible value of a → b → c → + a → b → d → + a → c → d → is equal to:

Options

  1. A- 42
  2. B- 40
  3. C- 29
  4. D- 38

Correct answer

A. - 42

Step-by-step solution

Given, a vector a → is coplanar with vectors b → = 2 i ^ + j ^ + k ^ and c → = i ^ - j ^ + k ^ and a → is perpendicular to d → = 3 i ^ + 2 j ^ + 6 k ^ , and | a → | = 10 . If a vector a → is coplanar with the vectors b →   &   c → then it can be expressed as the linear combination of the vectors. Thus, a → = λ b → + μ c → ⇒ a → = λ 2 i ^ + j ^ + k + μ i ^ - j ^ + k ⇒ a → = i ^ 2 λ +

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