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JEE Main20252 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The line L₁ is parallel to the vector a =-3 i +2 j +4 k and passes through the point (7,6,2) and the line L₂ is parallel to the vector b =2 i + j +3 k and passes through the point (5,3,4) . The shortest distance between the lines L₁ and L₂ is :

Options

  1. A23 38
  2. B21 57
  3. C23 57
  4. D21 38

Correct answer

A. 23 38

Step-by-step solution

aligned & L₁:(7 i +6 j +2 k)+ (-3 i +2 j +4 k) & L₂:(5 i +3 j +4 k)+ (2 i + j +3 k) aligned Distance between skew lines aligned & = (2 i +3 j -2 k ) (2 i +17 j -7 k ) 342 & = 69 342 = 69 3 38 = 23 38 aligned

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