Q82 / 180 · COMEDK 2014 · Mathematics
From a point $P(a, b, c)$ perpendicular $P A, P B$ are drawn to $y z$ and $z x$ planes. Find the equation of the plane $O A B$, where $O$ is the origin.
- A$b c x+c a y+a b z=0$
- Correct answerB$b c x+c a y-a b z=0$
- C$b c x-c a y+a b z=0$
- D$-b c x+c a y+a b z=0$
Solution
$P(a, b, c)$ and $P A$ and $P B$ are perpendicular to $Y Z$ and $Z X$ planes. Hence, coordinate of $A$ and $B$ are $(0, b, c)$ and $(a, 0, c)$ respectively.
Equation of plane passing through $(0,0,0),(0, b, c)$ and
$$
\begin{aligned}
&(a, 0, c) \text { is }\left|\begin{array}{lll}
x & y & z \\
0 & b & c \\
a & 0 & c
\end{array}\right|=0 \\
&\Rightarrow \quad x(b c-0)-y(0-a c)+z(0-a b)=0 \\
&\Rightarrow \quad b c x+a c y-a b z=0
\end{aligned}
$$
Hence, the correct answer is option: 'B'.