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AP EAMCET202315 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The distance between two parallel planes a x+b y+c z+d₁=0 , a x+b y+c z+d₂=0 is given by |d₁-d₂ | a^2+b^2+c^2 . If the plane 2 x-y+2 z+3=0 has the distances 1 3 and 2 3 units from the planes 4 x-2 y+4 z+ =0 and 2 x-y+2 z+ =0 respectively, then the maximum value of + is

Options

  1. A15
  2. B5
  3. C13
  4. D9

Correct answer

C. 13

Step-by-step solution

Given equation are 2 x-y+2 z+3=0...(1) and 4 x-2 y+4 z+ =0 2 x-y+2 z+ 2 =0...(2) and 2 x-y+2 z+ =0...(3) Since distance between equation (1) and (2) is 1 3 . Hence, | 2 -3 | 4+1+4 = 1 3 =8 Since distance between equation (1) and (3) is 2 3 . Hence, | -3| 4+1+4 = 2 3 =5 Therefore + =8+5=13

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