Question

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

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each pair

• For $\overleftrightarrow{NO}$ and $\overleftrightarrow{NQ}$: They intersect at point $N$, so they are not skew.
• For $\overleftrightarrow{JK}$ and $\overleftrightarrow{LP}$: They are non - parallel and do not intersect as they lie in different non - intersecting planes, so they are skew.
• For $\overleftrightarrow{KO}$ and $\overleftrightarrow{NO}$: They intersect at point $O$, so they are not skew.
• For $\overleftrightarrow{JN}$ and $\overleftrightarrow{OP}$: They are non - parallel and do not intersect as they lie in different non - intersecting planes, so they are skew.

Answer:

$\overleftrightarrow{JK}$ and $\overleftrightarrow{LP}$, $\overleftrightarrow{JN}$ and $\overleftrightarrow{OP}$