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MHT CET202616 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The lines x - 1 -1 = y + 2 1 = z - 3 -2 and x - 1 1 = y + 2 1 = z + 1 -2 are

Options

  1. Aintersecting but not perpendicular
  2. Bparallel
  3. Cperpendicular
  4. Dskew lines

Correct answer

D. skew lines

Step-by-step solution

The direction ratios of the given lines are b ₁ = - i + j - 2 k and b ₂ = i + j - 2 k . The lines pass through the points a ₁ = i - 2 j + 3 k and a ₂ = i - 2 j - k . The vector connecting the points is a ₂ - a ₁ = -4 k . The cross product of the direction vectors is: b ₁ b ₂ = vmatrix i & j & k -1 & 1 & -2 1 & 1 & -2 vmatrix = 0 i - 4 j - 2 k Now, we find the scalar triple product ( a ₂ - a ₁) ( b ₁ b ₂) : ( a ₂ - a ₁) ( b ₁ b ₂) = (-4 k ) (-4 j - 2 k ) = 8 0 Since the scalar triple product is non-zero, the shortes

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