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 $\overleftrightarrow{MQ}$ and $\overleftrightarrow{OP}$: They are non - parallel and do not intersect as they lie in different non - parallel planes.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{QT}$: They are non - parallel and do not intersect as they are in different non - parallel planes.
• For $\overleftrightarrow{QT}$ and $\overleftrightarrow{OP}$: They are non - parallel and do not intersect as they are in different non - parallel planes.
• For $\overleftrightarrow{ST}$ and $\overleftrightarrow{MQ}$: They are non - parallel and do not intersect as they are in different non - parallel planes.

Answer:

$\overleftrightarrow{MQ}$ and $\overleftrightarrow{OP}$, $\overleftrightarrow{NR}$ and $\overleftrightarrow{QT}$, $\overleftrightarrow{QT}$ and $\overleftrightarrow{OP}$, $\overleftrightarrow{ST}$ and $\overleftrightarrow{MQ}$