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JEE Main20248 Apr 2024Evening ShiftMathematicsThree Dimensional GeometryActual

If the shortest distance between the lines x- 2 = y-4 3 = z-3 4 and x-2 4 = y-4 6 = z-7 8 is 13 29 , then a value of is :

Options

  1. A-1
  2. B- 13 25
  3. C13 25
  4. D1

Correct answer

D. 1

Step-by-step solution

. array l r ₁=( i +4 j +3 k )+ (2 i +3 j +4 k ) r ₂=(2 i +4 j +7 k )+ (2 i +3 j +4 k ) array gathered b =2 i +3 j +4 k a ₂+ i +4 j +3 k a ₂=2 i +4 j +7 k gathered Shortest dist. = | b ( a ₂- a ₁ ) | | b | = 13 29 aligned & , |(2 i +3 j +4 k ) ((2- ) i +4 k )| 29 = 13 29 . & |-8 j -3(2- ) k +12 i +4(2- ) j |=13 & |12 i -4 j +(3 -6) k |=13 aligned aligned & 144+16 ^2+(3 -6)^2=169 & 16 ^2+(3 -6)^2=25= =1 aligned

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