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JEE Advanced2012MathematicsThree Dimensional GeometryActual

If the straight lines x-1 2 = y+1 k = z 2 and x+1 5 = y+1 2 = z k are coplanar, then the plane (s) containing these two lines is (are)

Options

  1. Ay+2 z=-1
  2. By+z=-1
  3. Cy-z=-1
  4. Dy-2 z=-1

Correct answer

B. y+z=-1

Step-by-step solution

Given that lines are coplanar. | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |= | array ccc 2 & 0 & 0 2 & k & 2 5 & 2 & k array |=0 k= 2 For k=2 , equation of the plane is given by | array ccc x-1 & y+1 & z 2 & 2 & 2 5 & 2 & 2 array |=0 y-z+1=0 For k=-2 , equation of the plane is given by | array ccc x-1 & y+1 & z 2 & -2 & 2 5 & 2 & -2 array |=0 y+z+1=0

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