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JEE Main202622 January 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let L be the line x+1 2 = y+1 3 = z+3 6 and let S be the set of all points ( a , b , c ) on L, whose distance from the line x+1 2 = y+1 3 = z-9 0 along the line L is 7. Then _ (a, b, c) S (a+b+c) is equal to :

Options

  1. A6
  2. B34
  3. C40
  4. D28

Correct answer

B. 34

Step-by-step solution

M is the point of intersection of L₁ & L₂ 2 - 1 = 2 - 1, 3 - 1 = 3 - 1, 6 - 3 = 9 = 2 = M(3, 5, 9) Now let point P be (2K - 1, 3K - 1, 6K - 3) on L₂ such that PM = 7 (2K - 4)^2 + (3K - 6)^2 + (6K - 12)^2 = 7 49K^2 + 196 - 196K = 49 K^2 + 4 - 4K = 1 K^2 - 4K + 3 = 0 K = 1, 3 So points P & Q are (1, 2, 3) & (5, 8, 15) So sum of all co-ordinates of P & Q = 34

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