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JEE Main20258 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let the values of for which the shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x- 3 = y-4 4 = z-5 5 is 1 6 be ₁ and ₂ . Then the radius of the circle passing through the points (0,0), ( ₁, ₂ ) and ( ₂, ₁ ) is

Options

  1. A5 2 3
  2. B4
  3. C2 3
  4. D3

Correct answer

A. 5 2 3

Step-by-step solution

aligned & p =2 i +3 j +4 k , q =3 i +4 j +5 k & p q = | array lll i & j & k 2 & 3 & 4 3 & 4 & 5 array |=- i +2 j - k & A (1,2,3) B ( , 4,5) & Shortest Distance = | AB ( P q ) | P q | | aligned aligned & 1 6 = | (( -1) i +2 j +2 k ) (- i +2 j - k ) 6 | & |- +1+4-2|=1 | -3|=1 & =3 1=4,2 aligned Radius of circle passing through points aligned & (0,0),(4,2) &(2,4) & = abc 4 = 20 20 8 4 1 2 | array lll 1 & 1 & 1 0 & 4 & 2 0 & 2 & 4 array | = 20 2 2 2 12 & = 5 2 3 aligned

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