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Question: Answered & Verified by Expert
If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is
MathematicsThree Dimensional GeometryAP EAMCETAP EAMCET 2004
Options:
  • A $2 x+y-3 z+6=0$
  • 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:
2017 Upvotes Verified Answer
The correct answer is: $2 x-y+3 z-14=0$


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
$$
\begin{array}{rlrl}
& 2(x-2)-1(y+1)+3(z-3) & =0 \\
\Rightarrow & 2 x-y+3 z-14 =0
\end{array}
$$

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