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JEE Main202523 Jan 2025Evening ShiftMathematicsThree Dimensional GeometryActual

If the square of the shortest distance between the lines x-2 1 = y-1 2 = z+3 -3 and x+1 2 = y+3 4 = z+5 -5 is m n , where m , n are coprime numbers, then m + n is equal to :

Options

  1. A21
  2. B9
  3. C14
  4. D6

Correct answer

B. 9

Step-by-step solution

aligned & a =(2,1,-3) & b =(-1,-3,-5) & p q = | array ccc i & j & k 1 & 2 & -3 2 & 4 & -5 array | & =2 i - j aligned aligned & b - a =-3 i -4 j -2 k & S _ d = |( b - a ) ( p q )| | p q | - & = 2 5 & ( ~S _ d )^2= 4 5 & ~m =4, n =5 ~m + n =9 aligned

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