Question

in the triangular prism shown below, which lines are parallel? mq and op qr and op qr and rs qs and np

Explanation:

Step1: Recall parallel - line definition in 3 - D.

In a triangular prism, parallel lines are lines that lie in the same plane and do not intersect.

Step2: Analyze each option.

• For $\overrightarrow{MQ}$ and $\overrightarrow{OP}$: They are not parallel as they are not in the same plane and do not have the right - orientation for parallelism.
• For $\overrightarrow{QR}$ and $\overrightarrow{OP}$: They are not parallel as they are in different non - parallel planes of the prism.
• For $\overrightarrow{QR}$ and $\overrightarrow{RS}$: They are adjacent sides of a triangular face, so they are not parallel.
• For $\overrightarrow{QS}$ and $\overrightarrow{NP}$: In a triangular prism, the opposite lateral edges are parallel. $\overrightarrow{QS}$ and $\overrightarrow{NP}$ are opposite lateral edges of the triangular prism, so they are parallel.

Answer:

$\overrightarrow{QS}$ and $\overrightarrow{NP}$