Question

in the cube shown below, which lines are intersecting? select all that apply. diagram of a cube with vertices labeled (e.g., t, q, x, n, o, s, r) and options: $overleftrightarrow{os}$ and $overleftrightarrow{pt}$, $overleftrightarrow{nr}$ and $overleftrightarrow{mq}$, $overleftrightarrow{os}$ and $overleftrightarrow{rs}$, $overleftrightarrow{rs}$ and $overleftrightarrow{no}$ (or similar labeled lines)

Explanation:

To determine which lines are intersecting, we analyze each pair:

Step 1: Analyze $\overrightarrow{OS}$ and $\overrightarrow{RS}$

In a cube, $\overrightarrow{OS}$ and $\overrightarrow{RS}$ meet at point $S$. So they intersect.

Step 2: Analyze other pairs (briefly)

• $\overrightarrow{OS}$ and $\overrightarrow{PT}$: These are skew (not intersecting, not parallel).
• $\overrightarrow{NR}$ and $\overrightarrow{MQ}$: These are parallel (in a cube, opposite edges are parallel), so not intersecting.
• $\overrightarrow{RS}$ and $\overrightarrow{NO}$: These are skew (different faces, no common point).

Answer:

$\boldsymbol{\overrightarrow{OS}}$ and $\boldsymbol{\overrightarrow{RS}}$