Answer
$ v $, $ v_1 $ and $ v_3$ are equivalent.
Work Step by Step
We have
$$ v=\overrightarrow{P_0Q_0}=Q_0-P_0=(0,1,-4)-(1,-2,5)=\langle -1,3,-9\rangle,$$
$$ v_1=\overrightarrow{P_0Q_0}=Q_0-P_0=(0,5,-5)-(1,2,4)=\langle -1,3,-9\rangle,$$
$$ v_2=\overrightarrow{P_0Q_0}=Q_0-P_0=(0,-8,13)-(1,5,4)=\langle -1,-13,-9\rangle,$$
$$ v_3=\overrightarrow{P_0Q_0}=Q_0-P_0=(-1,3,-9)-(0,0,0)=\langle -1,3,-9 \rangle,$$
$$ v_4=\overrightarrow{P_0Q_0}=Q_0-P_0=(1,7,4)-(2,4,5)=\langle -1,3,-1 \rangle.$$
Hence, $ v $, $ v_1 $ and $ v_3$ are equivalent.
