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 ?
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.