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Question:
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Consider the following planes
$$
\begin{aligned}
& P: x+y-2 z+7=0 \\
& Q: x+y+2 z+2=0 \\
& R: 3 x+3 y-6 z-11=0
\end{aligned}
$$
Options:
$$
\begin{aligned}
& P: x+y-2 z+7=0 \\
& Q: x+y+2 z+2=0 \\
& R: 3 x+3 y-6 z-11=0
\end{aligned}
$$
Solution:
1909 Upvotes
Verified Answer
The correct answer is:
$P$ and $R$ are parallel
$P$ and $R$ are parallel
Given planes are
$$
\begin{aligned}
& P: x+y-2 z+7=0 \\
& Q: x+y+2 z+2=0
\end{aligned}
$$
and $R: 3 x+3 y-6 z-11=0$
Consider Plane $P$ and $R$.
Here $a_1=1, b_1=1, c_1=-2$ and $a_2=3, b_2=3, c_2=-6$
Since, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{3}$ therefore $P$ and $R$ are parallel.
$$
\begin{aligned}
& P: x+y-2 z+7=0 \\
& Q: x+y+2 z+2=0
\end{aligned}
$$
and $R: 3 x+3 y-6 z-11=0$
Consider Plane $P$ and $R$.
Here $a_1=1, b_1=1, c_1=-2$ and $a_2=3, b_2=3, c_2=-6$
Since, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{3}$ therefore $P$ and $R$ are parallel.
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