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AP EAMCET202421 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the skew lines r =(2 i - j )+t( i +2 k ) and r =(-2 i + k )+s( i - j - k ) is

Options

  1. A3 2 7
  2. B3 7
  3. C3 14
  4. D4 14

Correct answer

A. 3 2 7

Step-by-step solution

aligned & r =(2 i - j )+t( i +2 k ) a ₁=2 i - j , b ₁= i +2 k & r =(-2 i + k )+s( i - j - k ) & a ₂=-2 i + k , b ₂= i - j - k & b ₁ b ₂= | array ccc i & j & k 1 & 0 & 2 1 & -1 & -1 array |=2 i +3 j - k & ( a ₂- a ₁ )=-4 i + j + k & Distance = | ( b ₁ b ₂ ) ( a ₂- a ₁ ) | b ₁ b ₂ | |= | -8+3-1 14 |= 3 2 7 aligned

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