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JEE Main202524 Jan 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let the line passing through the points (-1,2,1) and parallel to the line x-1 2 = y+1 3 = z 4 intersect the line x+2 3 = y-3 2 = z-4 1 at the point P . Then the distance of P from the point Q(4,-5,1) is

Options

  1. A5
  2. B5 5
  3. C5 6
  4. D10

Correct answer

B. 5 5

Step-by-step solution

Equation of line through point (-1,2,1) is aligned & x+1 2 = y-2 3 = z-1 4 = -(2) & So, [ array l x=2 -1 y=3 +2 z=4 +1 array . aligned By (1) x+2 3 = y-3 2 = z-4 1 = ( Let ) So, [ array l x=3 -2 y=2 +3 z= +4 array . For intersection point ' P ' aligned & x =2 -1=3 -2 & y =3 +2=2 +3 & z =4 +1= +4 aligned So, point P ( x , y , z )=(1,5,5) & Q (4,-5,1) aligned & P Q= 9+100+16 & = 125 =5 5 aligned

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