Question

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

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze $\overrightarrow{QU}$ and $\overrightarrow{SV}$

$\overrightarrow{QU}$ and $\overrightarrow{SV}$ are non - parallel and do not intersect as they lie in different non - parallel planes.

Step3: Analyze $\overrightarrow{PT}$ and $\overrightarrow{UV}$

$\overrightarrow{PT}$ and $\overrightarrow{UV}$ are non - parallel and do not intersect as they lie in different non - parallel planes.

Step4: Analyze $\overrightarrow{OR}$ and $\overrightarrow{SV}$

$\overrightarrow{OR}$ and $\overrightarrow{SV}$ are parallel as they are in parallel planes and have the same direction, so they are not skew.

Step5: Analyze $\overrightarrow{PQ}$ and $\overrightarrow{UV}$

$\overrightarrow{PQ}$ and $\overrightarrow{UV}$ are non - parallel and do not intersect as they lie in different non - parallel planes.

Answer:

$\overrightarrow{QU}$ and $\overrightarrow{SV}$, $\overrightarrow{PT}$ and $\overrightarrow{UV}$, $\overrightarrow{PQ}$ and $\overrightarrow{UV}$