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The lines x -2 1 = y -3 1 = z -4 - k and x -1 k = y -4 1 = 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

| array ccc x ₂- x ₁ & y ₂- y ₁ & z ₂- z ₁ l ₁ & ~m ₁ & n ₁ l ₂ & ~m ₂ & n ₂ array |=0 | array ccc 1 & -1 & -1 1 & 1 & - k k & 2 & 1 array |=0 | array ccc 0 & 0 & -1 2 & 1+ k & - k k +2 & 1 & 1 array |=0 k ^2+3 k ^2=0 k ( k +3)=0 or k =0 or -3

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