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JEE Main202126 Feb 2021Morning ShiftMathematicsVector AlgebraActual

If 1 , 5 , 35 , 7 , 5 , 5 , 1 , λ , 7 and 2 λ , 1 , 2 are coplanar, then the sum of all possible values of λ is:

Options

  1. A44 5
  2. B- 44 5
  3. C39 5
  4. D- 39 5

Correct answer

A. 44 5

Step-by-step solution

A 1 , 5 , 35 , B 7 , 5 , 5 , C 1 , λ , 7 , D 2 λ , 1 , 2 A B ¯ = 6 i ^ - 30 k ^ ,   B C ¯ = - 6 i + ^ λ - 5 j ^ + 2 k ^ C D → = 2 λ - 1 i ^ + 1 - λ j ^ - 5 k ^ Points are coplanar ⇒ 0 = 6 0 - 30 - 6 λ - 5 2 2 λ - 1 1 - λ - 5 = 6 - 5 λ + 25 - 2 + 2 λ - 30 - 6 + 6 λ - 2 λ 2 - λ - 10 λ + 5 = 6 - 3 λ + 23 - 30 - 2 λ 2 + 11 λ - 5 - 6 + 6 λ = 6 - 3 λ + 23 - 30 - 2 λ 2 + 17 λ - 11 = 6 - 3 &#9

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