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JEE Main20253 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Line L₁ passes through the point (1,2,3) and is parallel to Z -axis. Line L ₂ passes through the point ( , 5,6) and is parallel to y -axis. Let for = ₁, ₂, ₂ ₁ , the shortest distance between the two lines be 3 . Then the square of the distance of the point ( ₁, ₂, 7 ) from the line L ₁ is

Options

  1. A40
  2. B32
  3. C25
  4. D37

Correct answer

C. 25

Step-by-step solution

aligned & L₁ x-1 0 = y-2 0 = z-3 1 & L₂ x- 0 = y-5 1 = z-6 0 aligned SD = | array ccc -1 & 3 & 3 0 & 0 & 1 0 & 1 & 0 array | | array ccc i & j & k 0 & 0 & 1 0 & 1 & 0 array | =| -1|=3 aligned & =4,-2 & ₁=4 & ₂=-2 aligned Let foot of perpendicular from aligned & P (4,-2,7) is Q (1,2, t +3) & So (3,-4,4- t ) (0,0,1)=0 & t =4 aligned aligned & So Q (1,2,7) & PQ ^2=9+16 & PQ ^2=25 aligned

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