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MHT CET20244 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if

Options

  1. Ak =1 or k =-1
  2. Bk =0 or k =-3
  3. Ck =3 or k =-3
  4. Dk =0 or k =3

Correct answer

B. k =0 or k =-3

Step-by-step solution

If the given lines are co-planar, we get | array ccc 2-1 & 3-4 & 4-5 1 & 1 & -k k & 2 & 1 array |=0 array ll & | array ccc 1 & -1 & -1 1 & 1 & -k k & 2 & 1 array |=0 & 1(1+2 k)+1 (1+k^2 )-1(2-k)=0 & 1+2 k+1+k^2-2+k=0 & k^2+3 k=0 & k=0 or k=-3 array

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