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TS EAMCET · Maths · Three 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

  1. A \(29 x+31 y+3 z=63\)
  2. B \(23 x+29 y-29 z=23\)
  3. C \(23 x+29 y+3 z=55\)
  4. D \(31 x+37 y+3 z=71\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(23 x+29 y+3 z=55\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} & 2001=3.23 .29 \\ & \text { so, } a=3, b=23, c=29 \end{aligned} \] Since, direction ratios of a normal are \(b, c, a\) then the equation of plane is \[ \begin{aligned} b x+c y+a z+d & =0 \\ \Rightarrow \quad 23 x+29 y+3 z+d & =0 \end{aligned} \] It…