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AP EAMCET202419 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the skew lines r (- i -2 j -3 k )+t(3 i -2 j -2 k ) and r =(7 i +4 k )+s( i -2 j +2 k ) is

Options

  1. A15
  2. B0
  3. C9
  4. D16

Correct answer

C. 9

Step-by-step solution

Given aligned & r =(- i -2 j -3 k )+t(3 i -2 j -2 k )= a ₁+t b ₁ & and r =(7 i +4 k )+s( i -2 j +2 k )= a ₂+s b ₂ aligned Now, b ₁ b ₂= | array ccc i & j & k 3 & -2 & -2 1 & -2 & 2 array |=-8 i -8 j -4 k Since, required shortest distance aligned & = | ( b ₁ b ₂ ) ( a ₂- a ₁ ) ( b ₁ b ₂ ) |= | (-8 i -8 j -4 k ) (8 i +2 j +7 k ) |-8 i -8 j -4 k | | & = | -64-16-28 12 |= 108 12 =9 . aligned

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