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JEE Main201912 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

Let S be the set of all real values of λ such that a plane passing through the points - λ 2 , 1 , 1 , 1 , - λ 2 , 1 and 1 , 1 , - λ 2 also passes through the point - 1 , - 1 , 1 . Then S is equal to :

Options

  1. A3
  2. B3 ,   - 3
  3. C1 , - 1
  4. D3 , - 3

Correct answer

D. 3 , - 3

Step-by-step solution

As we know that if four points P ,   A ,   B ,   C are coplanar, the vectors P A → ,   P B → ,   P C → must be coplanar. ⇒ P A → . P B → × P C → = 0 ⇒ - λ   2 + 1 2 0 2 - λ 2 + 1 0 2 2 - λ 2 - 1 = 0 ⇒ - λ 2 + 1 - λ 2 + 1 - λ 2 - 1 - 0 - 2 2 - λ 2 - 1 - 0 + 0 4 - 2 - λ 2 + 1 = 0 ⇒ - λ 2 + 1 λ 4 - 1 + 4 λ 2 + 1 = 0 ⇒ - λ 2 + 1 λ 2 + 1 λ 2 - 1 + 4

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