Question

in the rectangular prism shown below, which lines are skew?

Explanation:

Step1: Recall skew - lines definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze each option

• For $\overrightarrow{KO}$ and $\overrightarrow{LP}$: They are in different planes and do not intersect and are not parallel.
• For $\overrightarrow{KN}$ and $\overrightarrow{LP}$: $\overrightarrow{KN}$ and $\overrightarrow{LP}$ are parallel as they are opposite sides of a rectangular face.
• For $\overrightarrow{NR}$ and $\overrightarrow{QR}$: $\overrightarrow{NR}$ and $\overrightarrow{QR}$ intersect at point $R$.
• For $\overrightarrow{KL}$ and (incomplete option in question, but based on the above analysis of the first option) we focus on $\overrightarrow{KO}$ and $\overrightarrow{LP}$ which meet the skew - lines criteria.

Answer:

$\overrightarrow{KO}$ and $\overrightarrow{LP}$