Answer
$-3 i+2j -k$
Work Step by Step
Let us consider $P_1$ and $P_2$ as vectors and, a vector $\overrightarrow{P_1P_2}$ can be found as:
$\overrightarrow{P_1P_2}=\overrightarrow{P_2}-\overrightarrow{P_1}=\lt 2,9,-2 \gt -\lt 5,7,-1 \gt =\lt -3,2,-1 \gt$
Hence, our final answers is: $\overrightarrow{P_1P_2}=-3 i+2j -k$
