Question

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

Explanation:

Step1: Recall definition of intersecting lines

Intersecting lines meet at a point.

Step2: Analyze each pair

• $\overrightarrow{OS}$ and $\overrightarrow{LM}$: They are parallel, do not intersect.
• $\overrightarrow{PS}$ and $\overrightarrow{RS}$: They meet at point $S$, so they are intersecting.
• $\overrightarrow{PQ}$ and $\overrightarrow{LP}$: They meet at point $P$, so they are intersecting.
• $\overrightarrow{QR}$ and $\overrightarrow{LP}$: They are skew - not parallel and do not intersect in 3 - D space.

Answer:

$\overrightarrow{PS}$ and $\overrightarrow{RS}$, $\overrightarrow{PQ}$ and $\overrightarrow{LP}$