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JEE Main202229 Jul 2022Evening ShiftMathematicsVector AlgebraActual

If 2 , 3 , 9 , 5 , 2 , 1 , 1 , λ , 8 and λ , 2 , 3 are coplanar, then the product of all possible values of λ is

Options

  1. A21 2
  2. B59 8
  3. C57 8
  4. D95 8

Correct answer

D. 95 8

Step-by-step solution

Given, Points A 2 , 3 , 9 ,   B 5 , 2 , 1 ,   C 1 , λ , 8   &   D λ , 2 , 3 are coplanar, Now we know that condition of coplanarity is A B → A C → A D → = 0 ⇒ 3 - 1 - 8 - 1 λ - 3 - 1 λ - 2 - 1 - 6 = 0 ⇒ 3 - 6 λ - 3 - 1 + 1 6 + λ - 2 - 8 1 - λ - 3 λ - 2 = 0 ⇒ 3 - 6 λ + 17 + 4 + λ - 8 + 8 λ - 3 λ - 2 = 0 ⇒ - 18 λ + 51 + 4 + λ - 8 + 8 λ 2 - 40 λ + 48 = 0 ⇒ 8 λ 2 -

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