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AP EAMCET201921 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the skew lines r =(6 i +2 j +2 k )+t( i -2 j +2 k ) and r =(-4 i - k )+s(3 i -2 j -2 k ) is

Options

  1. A9
  2. B40 7
  3. C108
  4. D120

Correct answer

A. 9

Step-by-step solution

Given, array ll & r =(6 i +2 j +2 k )+t( i -2 j +2 k ) and & r =(-4 i - k )+s(3 i -2 j -2 k ) Here, & a =6 i +2 j +2 k , b = i -2 j +2 k & c =-4 i - k , d =3 i -2 j -2 k array aligned & Now, b d = | array ccc i & j & k 1 & -2 & 2 3 & -2 & -2 array | & = i (4+4)- j (-2-6)+ k (-2+6)=8 i +8 j +4 k aligned By Eq. (i), aligned & = | (10 i +2 j +3 k ) (8 i +8 j +4 k ) 64+64+16 | & = | 80+16+12 144 |= 108 12 =9 aligned

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