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JEE Main20249 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let the line L intersect the lines x-2=-y=z-1,2(x+1)=2(y-1)=z+1 and be parallel to the line x-2 3 = y-1 1 = z-2 2 . Then which of the following points lies on L?

Options

  1. A(- 1 3 , 1,-1 )
  2. B(- 1 3 ,-1,1 )
  3. C(- 1 3 , 1,1 )
  4. D(- 1 3 ,-1,-1 )

Correct answer

A. (- 1 3 , 1,-1 )

Step-by-step solution

L ₁: x -2 1 = y -1 = z -1 1 = L ₂: x +1 1 2 = y -1 1 2 = z +1 1 = dr of line MN will be & it will be proportional to =- 4 3 & =- 2 3 Coordinate of M will be < ( 2 3 , 4 3 ,- 1 3 ) and equation of required line will be. x - 2 3 3 = y - 4 3 1 = z + 1 3 2 = k So any point on this line will be aligned & ( 2 3 +3 k , 4 3 + k ,- 1 3 +2 k ) & 2 3 +3 k =- 1 3 k =- 1 3 aligned Point lie on the line for k =- 1 3 is (- 1 3 , 1,-1 )

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