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MHT CET2019Evening ShiftMathematicsThree Dimensional GeometryActual

If P 6,10,10 , Q 1,0 , - 5 , R 6 , - 10 , λ are vertices of a triangle right angled at Q, then value of λ is ….

Options

  1. A0
  2. B1
  3. C3
  4. D2

Correct answer

A. 0

Step-by-step solution

In Δ P Q R is right angled, at θ ∴ P R 2 = P Q 2 + R Q 2 ⇒ 6 - 6 2 + - 10 - 10 2 + λ - 10 2 + 1 - 6 2 + 0 - 10 2 + - 5 - 10 2 = 1 - 6 2 + 0 + 10 2 + - 5 - λ 2 ⇒ 400 + λ 2 + 100 - 20 λ = 25 + 100 + 225 + 25 + 100 + 25 + λ 2 + 10 λ ⇒ λ 2 - 20 λ + 500 = 350 + 150 + 10 λ + λ 2 ⇒ - 20 λ = 10 λ ⇒ 30 λ = 0 ⇒ λ = 0

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