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MHT CET202123 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The distance between the parallel lines x-2 2 = y-4 5 = z-1 2 and x-1 3 = y+1 5 = z+3 2 is

Options

  1. A1 38 units
  2. B333 38 units
  3. C300 37 units
  4. D300 35 units

Correct answer

B. 333 38 units

Step-by-step solution

Let a ₁=2 i +4 j + k and a ₂= i -2 j -3 k a ₂- a ₁=- i -6 j -4 k and let b =3 i +5 j +2 k aligned & b | a ₂- a ₁ |= | array ccc i & j & k 3 & 5 & 2 -1 & -6 & -4 array |= i (-20+12)- j (-12+2)+ k (-18+5) & =-8 i +10 j -13 k & | b ( a ₂- a ₁ ) |= 64+100+169 = 133 aligned Also | b |= 9+25+4 = 38 Distance between given lines = 333 38 units

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