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AP EAMCET2003MathematicsThree Dimensional Geometry

The equation of the plane passing through (1,1,1) and (1,-1,-1) and perpendicular to 2 x-y+z+5=0 is :

Options

  1. A2 x+5 y+z+8=0
  2. Bx+y-z-1=0
  3. C2 x+5 y+z+4=0
  4. Dx-y+z-1=0

Correct answer

B. x+y-z-1=0

Step-by-step solution

Let the equation of plane passing through (1,1,1) is a(x-1)+b(y-1)+c(z-1)=0 (i) It is also passing through (1,-1,-1) . a(0)+b(-2)+c(-2)=0 or b+c=0 (ii) Since, Eq. (i) is perpendicular to the plane 2 x-y+z+5=0 2 a-b+c=0 (iii) Since, Eqs. (ii) and (iii) are identical a -2-2 = b -4-0 = c 4 a -4 = b -4 = c 4 Required equation of plane is x+y-z-1=0

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