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JEE Main202529 Jan 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the foot of the perpendicular from the point (1,2,2) on the line L : x-1 1 = y+1 -1 = z-2 2 . Let the line r =(- i + j -2 k )+ ( i - j + k ), R , intersect the line L at Q . Then 2( PQ )^2 is equal to :

Options

  1. A25
  2. B19
  3. C29
  4. D27

Correct answer

D. 27

Step-by-step solution

General point on line L : x-1 1 = y+1 -1 = z-2 2 is ( +1,- -1,2 +2) DR's of PM are ( ,- -3,2 )P M L aligned & +(-1)(- -3)+2(2 )=0 & 6 +3=0 aligned P ( 1 2 , -1 2 , 1 ) Let another line L^ : x+1 1 = y-1 -1 = z+2 1 General point on line L^ is ( -1,- +1, -2) Point of intersection of line L and L^ is array l|l +1= -1 & 2 +2= -2 - =2 (1) & 2 = -4 array aligned & Q(-1,1,-2) & 2(P Q)^2=2 ( ( 1 2 +1 )^2+ ( -1 2 -1 )^2+(1+2)^2 ) & =2 ( 9 4 + 9 4 +9 ) & =27 aligned

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