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JEE Main2015MathematicsThree Dimensional GeometryActual

If the points 1 , 1 , λ & ( - 3 , 0 , 1 ) , are equidistant from the plane, 3 x + 4 y - 12 z + 13 = 0 , then λ satisfies the equation:

Options

  1. A3 x 2 + 10 x + 7 = 0
  2. B3 x 2 + 10 x - 13 = 0
  3. C3 x 2 - 10 x + 7 = 0
  4. D3 x 2 - 10 x + 21 = 0

Correct answer

C. 3 x 2 - 10 x + 7 = 0

Step-by-step solution

1 ,   1 ,   λ   a n d   - 3 ,   0 ,   1 are equidistant from 3 x + 4 y - 12 z + 13 = 0 then 3 + 4 - 12 λ + 13 3 2 + 4 2 + 12 2 =   - 9 + 0 - 12 + 13 3 2 + 4 2 + 12 2 20 - 12 λ =   - 8 5 - 3 λ   =   - 2 25 - 30 λ + 9 λ 2 = 4   9 λ 2 - 30 λ + 21 = 0 3 λ 2 - 10 λ + 7 = 0

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