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AP EAMCET2002MathematicsThree Dimensional Geometry

A plane x passes through the point (1,1,1) . If b, c, a are the direction ratios of a normal to the plane, where a, b, c(a < b < c) are the factors of 2001 , then the equation of the plane is

Options

  1. A29 x+31 y+3 z=63
  2. B23 x+29 y-29 z=23
  3. C23 x+29 y+3 z=55
  4. D31 x+37 y+3 z=71

Correct answer

C. 23 x+29 y+3 z=55

Step-by-step solution

We have, aligned & 2001=3.23 .29 & so, a=3, b=23, c=29 aligned Since, direction ratios of a normal are b, c, a then the equation of plane is aligned b x+c y+a z+d & =0 23 x+29 y+3 z+d & =0 aligned It passes through (1,1,1) aligned & 23+29+3+d=0 & 55+d=0 & d=-55 & aligned Thus, equation of the plane is aligned & 23 x+29 y+3 z-55=0 & 23 x+29 y+3 z=55 & aligned

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