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JEE Main20245 Apr 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let d be the distance of the point of intersection of the lines x+6 3 = y 2 = z+1 1 and x-7 4 = y-9 3 = z-4 2 from the point (7,8,9) . Then d ^2+6 is equal to :

Options

  1. A69
  2. B78
  3. C72
  4. D75

Correct answer

D. 75

Step-by-step solution

aligned & x+6 3 = y 2 = z+1 1 = ....(1) & x=3 -6, y=2 , z= -1 & x-7 4 = y-9 3 = z-4 2 = ....(2) aligned x =4 +7, y =3 +9, z =2 +43 -6=4 +7 3 -4 =13 (3) 22 =3 +9 2 -3 =9 (4) 3 array c 6 -8 =26 6 -9 =27 - + - =-1 array gathered 3 -4(-1)=13 3 =9 =3 gathered int. point (3,6,2) ;(7,8,9) d ^2=16+4+49=69 Ans. d ^2+6=69+6=75

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