smc

Using vector addition can help solve this problem quickly. Note that algebraically, adding $\overrightarrow{OP}$ to $\overrightarrow{OQ}$ will give $\overrightarrow{OR}$. One method of vector addition is literally known as the "parallelogram rule" - if you are given $\overrightarrow{OP}$ and $\overrightarrow{OQ}$, to find $\overrightarrow{OR}$, you can literally draw a parallelogram, making a line though $P$ parallel to $OQ$, and a line through $Q$ parallel to $OP$. The intersection of those lines will give the fourth point $R$, and that fourth point will form a parallelogram with $O,P,Q$. Thus, $1$ is a possibility. Case $2$ is also a possibility, if $O,P,Q$ are collinear, then $R$ is also on that line. Since $OP\parallel QR$ and $PQ\parallel RO$, which can be seen from either the prior reasoning or by examining slopes, the figure can never be a trapezoid, which requires exactly one of parallel sides. Thus, the answer is $\boxed{\text{(1) or (2) only}}$