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Manipal MET2020MathematicsThree Dimensional Geometry

Equation of a plane passing through (-1,1,1) and (1,-1,1) and perpendicular to x+2 y+2 z=5 is

Options

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

Correct answer

C. 2 x+2 y-3 z+3=0

Step-by-step solution

Equation of plane passing through (-1,1,1) is a(x+1)+b(y-1)+c(z-1)=0 ....(i) Also, it is passing through (1,-1,1) . a(1+1)+b(-1-1)+c(1-1)=0 2 a-2 b+0 c=0 ....(ii) Also, required equation of plane (i) is perpendicular to x+2 y+2 z=5 . a 1+b 2+c 2=0 a+2 b+2 c=0 Eqs. (ii) and (iii) are identical. a -4-0 = -b 4-0 = c 4+2 a -4 = b -4 = c 6 a -2 = b -2 = c 3 = (say) a=-2 , b=-2 , c=3 On putting the values of a, b and c in Eq. (i), we get -2 (x+1)-2 (y-1)+3 (z-1)=0 [-2 x-2-2 y+2+3 z-3]=0 -2 x-2 y+3 z-3=0 2 x+2 y-3 z+3=0

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