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MHT CET20242 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the line x-3 2 = y+2 -1 = z+4 3 lies in the plane x+ m y- z =9 , then ^2+ m ^2 is

Options

  1. A1
  2. B4
  3. C2
  4. D5

Correct answer

C. 2

Step-by-step solution

Line is perpendicular to normal of plane aligned & (2 i - j +3 k ) (l i + m j - k )=0 & 2 l- m -3=0 aligned (3,-2,-4) lies on the plane l x+m y-z=9 array ll & 3 l-2 ~m +4=9 & 3 l-2 ~m =5 array Solving (i) and (ii), we get array ll & l=1, ~m =-1 & l^2+ m ^2=2 array

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