Question

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

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 pair

• For $\overrightarrow{GK}$ and $\overrightarrow{DH}$: $\overrightarrow{GK}$ and $\overrightarrow{DH}$ are parallel. They are opposite edges of the cube, and they are in parallel planes and do not intersect.
• For $\overrightarrow{FJ}$ and $\overrightarrow{DH}$: $\overrightarrow{FJ}$ and $\overrightarrow{DH}$ are not parallel. They are not in parallel planes and will not have the same direction - vector relationship.
• For $\overrightarrow{FJ}$ and $\overrightarrow{EI}$: $\overrightarrow{FJ}$ and $\overrightarrow{EI}$ are parallel. They are opposite edges of the cube, lying in parallel planes and never intersecting.
• For $\overrightarrow{FJ}$ and $\overrightarrow{DG}$: $\overrightarrow{FJ}$ and $\overrightarrow{DG}$ are not parallel. They are not in parallel planes and do not have the correct orientation for parallelism.

Answer:

$\overrightarrow{GK}$ and $\overrightarrow{DH}$, $\overrightarrow{FJ}$ and $\overrightarrow{EI}$