Consider the three planes $$
\begin{aligned}
& P_1: 3 x+15 y+21 z=9 \\
& P_2: x \cdot 3 y \cdot z=5, \text { and } \\
& P_3: 2 x+10 y+14 z=5
\end{aligned}
$$
Then, which one of the following is true?
Select the correct option:
A
$P_1$ and $P_2$ are parallel
B
$P_1$ and $P_3$ are parallel
C
$P_2$ and $P_3$ are parallel
D
$\mathrm{P}_1, \mathrm{P}_2$ and $\mathrm{P}_3$ all are parallel
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$
\begin{aligned}
& P_1: x+5 y+7 z=3 \\
& P_2: x \cdot 3 y \cdot z=5 \\
& P_3: x+5 y+7 z=\frac{5}{2}
\end{aligned}
$$
so $P_1$ and $P_3$ are parallel.
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