Q93 / 160 · TS EAMCET 2004 · Mathematics

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

  • A
    $2 x+y-3 z+6=0$
  • Correct answer
    B
    $2 x-y+3 z-14=0$
  • C
    $2 x-y+3 z-13=0$
  • D
    $2 x+y+3 z-10=0$

Solution

Figure
Where $a, b, c$ are the direction ratios. Since, point $O(0,0,0$,$) is perpendicular to the foot of$ the plane at a point $P(2,-1,3)$. $\therefore \quad$ Direction's of $O P=2,-1,3$ Since the line $O P$ is perpendicular to the plane, therefore the direction's of the normal to the plane is proportional to the direction is of $O P$ $\therefore$ Required equation of plane is $$ \begin{array}{rlrl} & 2(x-2)-1(y+1)+3(z-3) & =0 \\ \Rightarrow & 2 x-y+3 z-14 =0 \end{array} $$

Hence, the correct answer is option: 'B'.

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