Answer
$P_2$ and $P_3$ are parallel; $P_1$ and $P_4$ are parallel.
Work Step by Step
Two planes are parallel when their normal vectors are parallel.
From the give problem, we see that $P_1$ has a normal vector $\lt 3,6,-3\gt$ or $3\lt 1,2,-1\gt $ and $P_4$ has normal vector $\lt 1,2,-1\gt $. They are parallel because they are multiples of each other.
Similarly, $P_2$ has normal vector $\lt 4,-12,8\gt $ and $P_4$ has normal vector $\lt 3,-9,6\gt $. These are also multiples and hence parallel.
