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NDA2026MathematicsThree Dimensional GeometryActual

Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What is the equation of the line L ?

Options

  1. A1-x=y+2=3-z
  2. B-(x+1)=y-2=z+3
  3. C3x+3=2y-4=6z+18
  4. D3x-3=2y+4=6z-18

Correct answer

C. 3x+3=2y-4=6z+18

Step-by-step solution

The line L is perpendicular to the plane 2x+3y+z+5=0 , so its direction ratios are proportional to the normal vector of the plane, which is (2, 3, 1) . The equation of the line passing through (-1, 2, -3) with direction ratios (2, 3, 1) is given by: x+1 2 = y-2 3 = z+3 1 Multiplying the entire equation by 6 , we get: 3(x+1) = 2(y-2) = 6(z+3) 3x+3 = 2y-4 = 6z+18 Answer: 3x+3=2y-4=6z+18

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