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MHT CET202410 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 equal to

Options

  1. A124 49
  2. B123 49
  3. C121 49
  4. D122 49

Correct answer

D. 122 49

Step-by-step solution

Line is perpendicular to normal to plane aligned & (2 i + j +3 k ) (l i + m j - k )=0 & 2 l+ m -3=0...(i) aligned (3,-2,-4) lies on the plane l x+ m y- z =9 aligned & 3 l-2 ~m +4=9 & 3 l-2 ~m =5...(ii) aligned Solving (i) and (ii), we get aligned & l= 11 7 , ~m = -1 7 & l^2+ m ^2 ( 11 7 )^2+ ( -1 7 )^2= 122 49 aligned

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