Question

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

Explanation:

Step1: Recall parallel - line definition

In a cube, parallel lines are lines that lie in the same plane and never intersect.

Step2: Analyze each option

• $\overrightarrow{LO}$ and $\overrightarrow{NO}$: These lines intersect at point $O$, so they are not parallel.
• $\overrightarrow{OS}$ and $\overrightarrow{NO}$: These lines are skew (not in the same plane and do not intersect), not parallel.
• $\overrightarrow{OS}$ and $\overrightarrow{MQ}$: In a cube, opposite - face diagonals in parallel planes are parallel. $\overrightarrow{OS}$ and $\overrightarrow{MQ}$ are in parallel planes and have the same direction - sense, so they are parallel.
• $\overrightarrow{PQ}$ and $\overrightarrow{LP}$: These lines intersect at point $P$, so they are not parallel.

Answer:

$\overrightarrow{OS}$ and $\overrightarrow{MQ}$