Question

in the cube shown below, which lines are parallel? (overrightarrow{pt}) and (overrightarrow{mp}) (overrightarrow{nr}) and (overrightarrow{no}) (overrightarrow{nr}) and (overrightarrow{os}) (overrightarrow{no}) and (overrightarrow{op})

Explanation:

Step1: Recall parallel - line property in cube

In a cube, parallel lines are lines that do not intersect and are in the same or parallel planes.

Step2: Analyze each option

• For $\overrightarrow{PT}$ and $\overrightarrow{MP}$, they are not parallel as they are in different non - parallel planes and will intersect if extended.
• For $\overrightarrow{NR}$ and $\overrightarrow{NO}$, they share a common point $N$ and thus are not parallel.
• For $\overrightarrow{NR}$ and $\overrightarrow{OS}$, in a cube, opposite edges are parallel. $\overrightarrow{NR}$ and $\overrightarrow{OS}$ are opposite edges of the cube, so they are parallel.
• For $\overrightarrow{NO}$ and $\overrightarrow{OP}$, they share a common point $O$ and are not parallel.

Answer:

$\overrightarrow{NR}$ and $\overrightarrow{OS}$