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JEE MainMathematicsThree Dimensional Geometry

If the lines x-1 2 = y-1 1 = z 1 and x-2 1 = y-4 -2 = z-3 -2 intersect at a point P , then the perpendicular distance from P to the plane 3x + 4y - 2 = 0 is :

Options

  1. A5
  2. B15
  3. C1
  4. D3

Correct answer

D. 3

Step-by-step solution

Let the coordinates of a general point on the first line be (2 +1, +1, ) . Let the coordinates of a general point on the second line be ( +2, -2 +4, -2 +3) . Since the lines intersect, these points must coincide for some values of and . Equating the coordinates, we get: 2 - = 1 + 2 = 3 + 2 = 3 Solving the first two equations: From the second equation, = 3 - 2 . Substituting into the first equation: 2(3 - 2 ) - = 1 6 - 5 = 1 5 = 5 = 1 . Then = 3 - 2(1) = 1 . Substituting = 1 into the general point of the first line,

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