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MHT CET202523 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines x-1 2 = y+1 3 = z-1 4 and x-3 1 = y-k 2 = z 1 intersect, then the value of k is

Options

  1. A3 2
  2. B- 3 2
  3. C9 2
  4. D- 2 9

Correct answer

C. 9 2

Step-by-step solution

The lines are parameterized as: Line 1: x-1 2 = y+1 3 = z-1 4 = Line 2: x-3 1 = y-k 2 = z 1 = General points on Line 1 are given by x = 2 + 1 , y = 3 - 1 , z = 4 + 1 , while points on Line 2 satisfy x = + 3 , y = 2 + k , z = . For intersection, the coordinates must be equal for some , . Equating x and z components gives the system: 2 - = 2 4 - = -1 Solving yields = - 3 2 , = -5 . Substituting into the y -coordinate equality 3 - 1 = 2 + k , we find k = 9 2 . The correct value is 9 2 .

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