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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The intercepts made on the x ,   y and z axes, by the plane which bisects the line joining the points 1,2 , 3 and - 3,4 , 5 at right angles, are a ,   b and c respectively, then the ordered triplet a , b , c is

Options

  1. A- 9 2 , 9,9
  2. B9 2 , 9,9
  3. C9 , - 9 2 , 9
  4. D9 , 9 2 , 9

Correct answer

A. - 9 2 , 9,9

Step-by-step solution

Let, equation of the plane is x a + y b + z c = 1 . Mid-point M of line joining P 1,2 , 3 and Q - 3,4 , 5 is - 1,3 , 4 . It lies on the plane i.e. - 1 a + 3 b + 4 c = 1 Also, P Q is parallel to the normal of the plane, so, 1 a - 4 = 1 b 2 = 1 c 2 = λ ⇒ 1 a = - 4 λ ,   1 b = 2 λ ,   1 c = 2 λ ⇒ 4 λ + 6 λ + 8 λ = 1 ⇒ λ = 1 18 i.e. a = - 9 2 ,   b = 9 ,   c = 9 Hence, ordered pair is - 9 2 , 9,9

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