Question

in the cube shown below, which lines are parallel? rs and rv rs and vw sw and vw st and tx

Explanation:

Step1: Recall parallel - line property in a cube

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

Step2: Analyze each option

• $\overrightarrow{RS}$ and $\overrightarrow{RV}$: $\overrightarrow{RS}$ and $\overrightarrow{RV}$ intersect at point $R$, so they are not parallel.
• $\overrightarrow{RS}$ and $\overrightarrow{VW}$: $\overrightarrow{RS}$ and $\overrightarrow{VW}$ are in parallel planes and do not intersect. They are parallel.
• $\overrightarrow{SW}$ and $\overrightarrow{VW}$: $\overrightarrow{SW}$ and $\overrightarrow{VW}$ intersect at point $W$, so they are not parallel.
• $\overrightarrow{ST}$ and $\overrightarrow{TX}$: $\overrightarrow{ST}$ and $\overrightarrow{TX}$ intersect at point $T$, so they are not parallel.

Answer:

$\overrightarrow{RS}$ and $\overrightarrow{VW}$