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COMEDK2022MathematicsThree Dimensional Geometry

The point of intersection of the lines x-1 1 = y-1 2 = z-2 3 and x-5 2 = y-2 1 =z is

Options

  1. A(1,-2,0)
  2. B(3,1,0)
  3. C(-2,-5,-7)
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Let the first line be x-1 1 = y-1 2 = z-2 3 = . Then any point on the first line is (1+ , 1+2 , 2+3 ) . Let the second line be x-5 2 = y-2 1 = z 1 = . Then any point on the second line is (5+2 , 2+ , ) . For the lines to intersect, there must exist and such that: 1+ = 5+2 - 2 = 4 (1) 1+2 = 2+ 2 - = 1 (2) 2+3 = (3) Substituting = 2+3 from (3) into (2): 2 - (2+3 ) = 1 - - 2 = 1 = -3 . Using = -3 in (3): = 2 + 3(-3) = 2 - 9 = -7 . Check these values in equation (1): - 2 = -3 - 2(-7) = -3 + 14 = 11 . Since 11 4 , the l

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