Question

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

Explanation:

Step1: Recall parallel - line property in 3 - D

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

Step2: Analyze $\overrightarrow{JN}$ and $\overrightarrow{LP}$

They are in parallel planes and have the same direction, so they are parallel.

Step3: Analyze $\overrightarrow{KL}$ and $\overrightarrow{OP}$

They are in parallel planes and have the same direction, so they are parallel.

Step4: Analyze $\overrightarrow{IM}$ and $\overrightarrow{KO}$

They are in parallel planes and have the same direction, so they are parallel.

Step5: Analyze $\overrightarrow{KL}$ and $\overrightarrow{LP}$

$\overrightarrow{KL}$ and $\overrightarrow{LP}$ are adjacent edges and intersect at point $L$, so they are not parallel.

Answer:

$\overrightarrow{JN}$ and $\overrightarrow{LP}$, $\overrightarrow{KL}$ and $\overrightarrow{OP}$, $\overrightarrow{IM}$ and $\overrightarrow{KO}$