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AP EAMCET201726 Apr 2017Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane through (4,4,0) and perpendicular to the planes 2 x+y+2 z+3=0 and 3 x+3 y+2 z-8=0 is

Options

  1. A4 x+3 y+3 z=28
  2. B4 x-2 y-3 z=8
  3. C4 x+2 y+3 z=24
  4. D4 x+2 y-3 z=24

Correct answer

B. 4 x-2 y-3 z=8

Step-by-step solution

Let DR's of normal to the plane is . Then, equation plane passing through (4,4,0)(r-a) . n=0a(x-4)+b(y-4)+c(z)=0 Since this plane is to the given planes. So, we get 2 a+b+2 c=0 and 3 a+3 b+2 c=0 By using cross-multiplication method, aligned & a 2-6 = -b 4-6 = c 6-3 & a -4 = b 2 = c 3 aligned So, the required equation of plane aligned & -4(x-4)+2(y-4)+3(z)=0 & -4 x+16+2 y-8+3 z=0 & 4 x-2 y-3 z=8 aligned

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