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MHT CET2017MathematicsThree Dimensional Geometry

If the distance of points 2 i ^ + 3 j ^ + λ k ^ from the plane r → ⋅ ( 3 i ^ + 2 j ^ + 6 k ^ ) = 13 is 5 units then λ =

Options

  1. A6 , - 17 3
  2. B6 , 17 3
  3. C- 6 , - 17 3
  4. D- 6 , 17 3

Correct answer

A. 6 , - 17 3

Step-by-step solution

Equation of plane r ¯ ⋅ 3 i ^ + 2 j ^ + 6 k ^ = 13 i . e . 3 x + 2 y + 6z - 13 = 0 Given point ( 2 , 3 , λ ) Distance of plane from the point = a x 1 + b y 1 + c z 1 + d a 2 + b 2 + c 2 ⇒ 5 = 3 2 + 2 3 + 6 λ - 13 9 + 4 + 36 ⇒ 5 = 6 λ - 1 7 ⇒ 6 λ - 1 = ± 35 ⇒ 6 λ = 36 , 6 λ = - 34 λ = 6 , λ = - 17 3

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