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BITSAT2018MathematicsThree Dimensional GeometryActual

If the planes r → · 2 i ^ - λ j ^ + 3 k ^ = 0 and r → · λ i ^ + 5 j ^ - k ^ = 5 are perpendicular to each other, then the value of λ 2 + λ is

Options

  1. A0
  2. B2
  3. C1
  4. D3

Correct answer

A. 0

Step-by-step solution

We have, r → · λ i ^ + 5 j ^ - k ^ = 5 r → · 2 i ^ - λ j ^ + 3 k ^ = 0 We know that two planes r → · n → 1 = d 1 and r → · n → 2 = d 2 are perpendicular if n → 1 · n → 2 = 0 Therefore, λ i ^ + 5 j ^ - k ^ · 2 i ^ - λ j ^ + 3 k ^ = 0 ⇒ 2 λ - 5 λ - 3 = 0 ⇒ - 3 λ - 3 = 0 ⇒ λ = - 1 Therefore, λ 2 + λ = 0

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