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JEE Main202226 Jul 2022Morning ShiftMathematicsThree Dimensional GeometryActual

The length of the perpendicular from the point 1 , - 2 , 5 on the line passing through 1 , 2 , 4 and parallel to the line x + y - z = 0 = x - 2 y + 3 z - 5 is:

Options

  1. A21 2
  2. B9 2
  3. C73 2
  4. D1

Correct answer

A. 21 2

Step-by-step solution

Given line is parallel to the line x + y - z = 0 = x - 2 y + 3 z - 5 is: So, direction ratio of the line = i ^ j ^ k ^ 1 1 - 1 1 - 2 3 = i ^ - 4 j ^ - 3 k ^ So, equation of line passing through 1 , 2 , 4 is r → = i ^ + 2 j ^ + 4 k ^ + λ i ^ - 4 j ^ - 3 k ^ Let A 1 , 2 , 4 , Q 1 , - 2 , 5 and P be 1 + λ , 2 - 4 λ , 4 - 3 λ Given   P Q → and line are perpendicular, So, P Q → · i ^ - 4 j ^ - 3 k ^ = 0 ⇒ λ i ^ + 4 - 4 λ j ^ - 1 + 3 λ k ^ . i ^ - 4 j ^

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