Consider the three planes
Question:

Consider the three planes

$P_{1}: 3 x+15 y+21 z=9$

$P_{2}: x-3 y-z=5$, and

$P_{3}: 2 x+10 y+14 z=5$

Then, which one of the following is true ?

1. $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ are parallel

2. $P_{1}$ and $P_{3}$ are parallel

3. $P_{2}$ and $P_{3}$ are parallel

4. $\mathrm{P}_{1}, \mathrm{P}_{2}$ and $\mathrm{P}_{3}$ all are parallel

Correct Option: , 2

Solution:

$P_{1}: x+5 y+7 z=3$

$P_{2}: x-3 y-z=5$

$P_{3}: x+5 y+7 z=\frac{5}{2}$

so $\mathrm{P}_{1}$ and $\mathrm{P}_{3}$ are parallel.