Question

in the rectangular prism shown below, which lines are skew?
ko and lp
kn and lp
nr and qr
kl and mn

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each option

• For $\overleftrightarrow{KO}$ and $\overleftrightarrow{LP}$: $\overleftrightarrow{KO}$ and $\overleftrightarrow{LP}$ are parallel. They lie in parallel planes and do not intersect.
• For $\overleftrightarrow{KN}$ and $\overleftrightarrow{LP}$: $\overleftrightarrow{KN}$ and $\overleftrightarrow{LP}$ are skew. They are not in the same plane, not parallel, and do not intersect.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{QR}$: $\overleftrightarrow{NR}$ and $\overleftrightarrow{QR}$ intersect at point $R$.
• For $\overleftrightarrow{KL}$ and $\overleftrightarrow{MN}$: $\overleftrightarrow{KL}$ and $\overleftrightarrow{MN}$ are parallel. They lie in parallel planes and do not intersect.

Answer:

$\overleftrightarrow{KN}$ and $\overleftrightarrow{LP}$