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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The perpendicular bisector of a line segment with end points 1,2 , 6 and - 3,6 , 2 passes through - 6,2 , 4 and has the equation of the form x + 6 l = y - 2 m = z - 4 n (Where l , m , n are integers, l is a prime number and l > 0 ), then the value of l m n - l + m + n equals to

Options

  1. A- 3
  2. B- 5
  3. C- 7
  4. D- 9

Correct answer

C. - 7

Step-by-step solution

Midpoint of the line segment is 1 - 3 1 , 2 + 6 2 , 6 + 2 2 ≡ - 1 ,4 , 4 Parallel vector to the required line = - 1 + 6 i ^ + 4 - 2 j ^ + 4 - 4 k ^ = 5 i ^ + 2 j ^ + 0 k ^ Hence, equation of the line is x + 6 5 - y - 2 2 = z - 4 0 ⇒ l = 5 ,   m = 2 ,   n = 0

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