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JEE Main20249 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x-3 4 = y+7 -11 = z-1 5 and x-5 3 = y-9 -6 = z+2 1 is:

Options

  1. A178 563
  2. B187 563
  3. C185 563
  4. D179 563

Correct answer

B. 187 563

Step-by-step solution

aligned & n = p q & n = | array ccc i & j & k 4 & -11 & 5 3 & -6 & 1 array |=19 i +11 j +9 k & S.d. = projection of AB on n & = | AB n | n | |= | (2 i +16 j -3 k ) (19 i +11 j +9 k ) 361+121+81 | & = 38+176-27 563 & S.d. = 187 563 aligned

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