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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Let A be the point 1 , 2 , 3 and B be a point on the line x - 1 - 2 = y + 1 3 = z - 5 4 = k . The value of k such that line A B is perpendicular to the plane 4x + 9 y - 18 z = 6 is

Options

  1. A- 2 5
  2. B1 5
  3. C2 5
  4. Dno such value of k is possible

Correct answer

C. 2 5

Step-by-step solution

Coordinates of the point B are 2 k + 1 , 3 k − 1 , 4 k + 5 A vector parallel to A B is − 2 k i ^ + 3 k − 3 j ^ + 4 k + 2 k ^ ∵ the line A B is perpendicular to the given plane Hence, - 2 k 4 = 3 k - 3 9 = 4 k + 2 - 18 - 18 k = 12 k - 1 2 k = 2 5

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