Question

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

Explanation:

Step1: Recall parallel - line property in cube

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

Step2: Analyze each option

• $\overrightarrow{QR}$ and $\overrightarrow{KN}$: In a cube, opposite - face edges are parallel. $\overrightarrow{QR}$ and $\overrightarrow{KN}$ are opposite - face edges, so they are parallel.
• $\overrightarrow{QR}$ and $\overrightarrow{PQ}$: $\overrightarrow{QR}$ and $\overrightarrow{PQ}$ are adjacent edges of a face of the cube and they intersect at point $Q$, so they are not parallel.
• $\overrightarrow{MR}$ and $\overrightarrow{LP}$: $\overrightarrow{MR}$ and $\overrightarrow{LP}$ are opposite - face non - parallel edges, so they are not parallel.
• $\overrightarrow{MR}$ and $\overrightarrow{MQ}$: $\overrightarrow{MR}$ and $\overrightarrow{MQ}$ are adjacent edges of a face of the cube and they intersect at point $M$, so they are not parallel.

Answer:

$\overrightarrow{QR}$ and $\overrightarrow{KN}$