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MHT CET2009MathematicsThree Dimensional Geometry

Equation of the plane passing through (-2,2,2) and (2,-2,-2) and perpendicular to the plane 9 x-13 y-3 z=0 is

Options

  1. A5 x+3 y+2 z=0
  2. B5 x-3 y+2 z=0
  3. C5 x-3 y-2 z=0
  4. D5 x+3 y-2 z=0

Correct answer

A. 5 x+3 y+2 z=0

Step-by-step solution

Any plane passing through (-2,2,2) is A(x+2)+B(y-2)+C(z-2)=0 It passes through (2,-2,-2) 4 A-4 B-4 C=0 It is parallel to 9 x-13 y-3 z=0 array lll & 9 A-13 B-3 C=0 & (ii) array Solving Eqs. (i) and (ii), aligned & A 12-52 = B -36+12 = C -52+36 A -40 = B -24 = C -16 aligned Required equation of plane is -40(x+2)-24(y-2)-16(z-2)=0 array lr & -40 x-80-24 y+48-16 z+32=0 & 40 x+24 y+16 z=0 & 5 x+3 y+2 z=0 array

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