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JEE Main202628 January 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the distances of the point (1,2, a) from the line x-1 1 = y 2 = z-1 1 along the lines L ₁: x-1 3 = y-2 4 = z-a b and L ₂: x-1 1 = y-2 4 = z-a c are equal, then a+b+c is equal to

Options

  1. A5
  2. B7
  3. C4
  4. D6

Correct answer

B. 7

Step-by-step solution

Line L : x-1 1 = y 2 = z-1 1 L₁ : x-1 3 = y-2 4 = z-a b = L₂ : x-1 1 = y-2 4 = z-a c = Point A(3 +1, 4 +2, b +a) lies on L : 3 1 = 4 +2 2 = b +a-1 1 = 1 , a + b - 1 = 3 a + b = 4 ...(1), A = (4, 6, 4) Point B( +1, 4 +2, c +a) lies on L : 2 = 4 +2 = -1 , a - c - 1 = -1 a = c ...(2), B = (0, -2, 0) Since PA = PB where P = (1, 2, a) : 9 + 16 + (a-4)^2 = 1 + 16 + a^2 a = 3 , so c = 3 , b = 1 a + b + c = 7

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