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AP EAMCET202418 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the distance between the planes 2 x+y+z+1=0 and 2 x+y+z+ =0 is 3 units, then product of all possible values of is

Options

  1. A-43
  2. B43
  3. C53
  4. D-53

Correct answer

D. -53

Step-by-step solution

Given two planes are 2 x+y+z+1=0 and 2 x+y+z+ =0 Since, these are parallel planes So, distance between them aligned & = |1- | 4+1+1 |1- | 6 =3 & |1- |=3 6 1- = 3 6 aligned =1-3 6 , 1+3 6 Now, product of all value of =(1-3 6 )(1+3 6 )=1-9 6=-53

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