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JEE Main20268 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 = y- 3 = z+5 6 is equal to:

Options

  1. A12 7
  2. B145 7
  3. C146 7
  4. D143 7

Correct answer

C. 146 7

Step-by-step solution

Since the point (1, , 2) lies on the line x-4 1 = y-9 2 = z-5 1 , we substitute its coordinates into the line equation: 1-4 1 = -9 2 = 2-5 1 -3 = -9 2 = -3 - 9 = -6 = 3 The direction ratios of the given line are (1, 2, 1) . The direction ratios of the perpendicular from ( , 2, 3) to (1, 3, 2) are (1- , 3-2, 2-3) = (1- , 1, -1) . Since the lines are perpendicular, their dot product is zero: 1(1- ) + 2(1) + 1(-1) = 0 1 - + 2 - 1 = 0 = 2 Substituting = 2 and = 3 into the equations of the two lines, we get: L₁: x-1 2 =

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