Question

in the rectangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall parallel - lines definition

In a rectangular prism, parallel lines are lines that never intersect and are in the same plane or in parallel planes.

Step2: Analyze each option

• $\overrightarrow{RV}$ and $\overrightarrow{SV}$ intersect at point $V$, so they are not parallel.
• $\overrightarrow{OS}$ and $\overrightarrow{UV}$: In a rectangular prism, opposite edges are parallel. $\overrightarrow{OS}$ and $\overrightarrow{UV}$ are opposite edges, so they are parallel.
• $\overrightarrow{OR}$ and $\overrightarrow{PQ}$: These two lines are in parallel planes and do not intersect, so they are parallel.
• $\overrightarrow{QR}$ and $\overrightarrow{QU}$ intersect at point $Q$, so they are not parallel.

Answer:

$\overrightarrow{OS}$ and $\overrightarrow{UV}$, $\overrightarrow{OR}$ and $\overrightarrow{PQ}$