Question

in the cube shown below, which lines are parallel? select all that apply. sw and uy rs and vy tu and vy st and tu

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

• For $\overrightarrow{SW}$ and $\overrightarrow{UY}$: They are not parallel as they are skew lines (not in the same plane and do not intersect).
• For $\overrightarrow{RS}$ and $\overrightarrow{VY}$: They are not parallel. $\overrightarrow{RS}$ is on the bottom - face and $\overrightarrow{VY}$ is on a side - face and a diagonal line.
• For $\overrightarrow{TU}$ and $\overrightarrow{VY}$: In a cube, opposite edges are parallel. $\overrightarrow{TU}$ and $\overrightarrow{VY}$ are opposite edges of the cube, so they are parallel.
• For $\overrightarrow{ST}$ and $\overrightarrow{TU}$: They are adjacent edges and intersect at point $T$, so they are not parallel.

Answer:

$\overrightarrow{TU}$ and $\overrightarrow{VY}$