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AP EAMCET · Maths · Three Dimensional Geometry

The equation of the plane passing through the point \((1,2,2)\) and perpendicular to the planes \(x-y+2 z=3\) and \(2 \mathrm{x}-2 \mathrm{y}+\mathrm{z}+12=0\), is

  1. A \(\mathrm{x}-2 \mathrm{y}+2 \mathrm{z}-1=0\)
  2. B \(2 \mathrm{x}-3 \mathrm{y}+4 \mathrm{z}-4=0\)
  3. C \(x+y+z-5=0\)
  4. D \(x+y-3=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x+y-3=0\)

Step-by-step Solution

Detailed explanation

The equation of plane passing through the point \((1,2,2)\) is \(a(x-1)+b(y-2)+c(z-2)=0\) ...(i) Since \(\mathrm{eq}^{\mathrm{n}}\) (i) is normal to the planes \(x-y+2 z=3\) and \(2 x-2 y+z+12=0\) \(\therefore a-b+2 c=0\) ...(ii) and \(2 a-2 b+c=0\) ...(iii) From…