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BITSAT2023MathematicsThree 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 =3 or -2
  2. Bk =0 or -1
  3. Ck =1 or -1
  4. Dk =0 or -3

Correct answer

D. k =0 or -3

Step-by-step solution

Two planes are coplanar if | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ l₁ & m₁ & n₁ l₂ & m₂ & n₂ array |=0 | array ccc 1 & -1 & -1 1 & 1 & -k k & 2 & 1 array |=0 Applying C ₂ C ₂+ C ₁, C ₃ C ₃+ C ₁ | array ccc 1 & 0 & 0 1 & 2 & 1-k k & k+2 & 1+k array |=0 1[2+2 k-(k+2)(1-k)]=0 2+2 k- (-k^2-k+2 )=0 k^2+3 k=0 k(k+3)=0

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