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JEE Main20262 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the point of intersection of the lines x+1 3 = y+a 5 = z+b+1 7 and x-2 1 = y-b 4 = z-2a 7 lies on xy -plane, then the value of a + b is :

Options

  1. A2
  2. B5
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

Let the point of intersection be (x, y, 0) since it lies on the xy -plane. For the first line, equating the coordinates to a parameter : x+1 3 = y+a 5 = 0+b+1 7 = This gives x = 3b+3 7 - 1 and y = 5b+5 7 - a . For the second line, equating the coordinates to a parameter : x-2 1 = y-b 4 = 0-2a 7 = This gives x = -2a 7 + 2 and y = -8a 7 + b . Equating the x -coordinates from both lines: 3b+3 7 - 1 = -2a 7 + 2 3b-4 7 = -2a+14 7 2a + 3b = 18 Equating the y -coordinates from both lines: 5b+5 7 - a = -8a 7 + b 5b + 5 - 7

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