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JEE Main202522 Jan 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let L ₁: x-1 2 = y-2 3 = z-3 4 and L ₂: x-2 3 = y-4 4 = z-5 5 be two lines. Then which of the following points lies on the line of the shortest distance between L₁ and L₂ ?

Options

  1. A( 14 3 ,-3, 22 3 )
  2. B(- 5 3 ,-7,1 )
  3. C(2,3, 1 3 )
  4. D( 8 3 ,-1, 1 3 )

Correct answer

A. ( 14 3 ,-3, 22 3 )

Step-by-step solution

aligned & L₁: x-1 2 = y-2 3 = z-3 4 & L₂: x-2 3 = y-4 4 = z-5 5 aligned aligned & P(2 +1,3 +2,4 +3) & Q(3 +2,4 +4,5 +5) aligned Dr's of P Q & P Q= | array lll i & j & k 2 & 3 & 4 3 & 4 & 5 array |=- i +2 j - k & 2 -3 -1 -1 = 3 -4 -2 2 = 4 -5 -2 -1 & = 1 3 = -1 6 & P ( 5 3 , 3, 13 3 ) Q ( 3 2 , 10 3 , 25 6 ) aligned Dr's P Q 1,-2,1 Line y- 5 3 1 = y-3 -2 = y- 13 3 1

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