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JEE Main20252 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let the vertices Q and R of the triangle P Q R lie on the line x+3 5 = y-1 2 = z+4 3 , Q R=5 and the coordinates of the point P be (0,2,3) . If the area of the triangle P Q R is m n then :

Options

  1. Am -5 21 n =0
  2. B2 ~m -5 21 n =0
  3. C5 ~m -2 21 n =0
  4. D5 m-21 2 n=0

Correct answer

B. 2 ~m -5 21 n =0

Step-by-step solution

M (5 -3,2 +1,3 -4) Drs of PM 5 -3,2 -1,3 -7 Drs of line L 5,2,3 PM L (5 -3) 5+(2 -1) 2+(3 -7) 3=0 =1 M (2,3,-1) P M= 4+1+16 = 21 Area = 1 2 5 21 = m n 2 ~m -5 21 n =0

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