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 $\overrightarrow{QR}$ and $\overrightarrow{SV}$

$\overrightarrow{QR}$ and $\overrightarrow{SV}$ are in different planes, not parallel, and do not intersect. They are skew.

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

$\overrightarrow{RV}$ and $\overrightarrow{UV}$ intersect at point $V$, so they are not skew.

Step4: Analyze $\overrightarrow{QR}$ and $\overrightarrow{TU}$

$\overrightarrow{QR}$ and $\overrightarrow{TU}$ are parallel, so they are not skew.

Step5: Analyze $\overrightarrow{QR}$ and $\overrightarrow{PT}$

$\overrightarrow{QR}$ and $\overrightarrow{PT}$ are in different planes, not parallel, and do not intersect. They are skew.

Answer:

$\overrightarrow{QR}$ and $\overrightarrow{SV}$, $\overrightarrow{QR}$ and $\overrightarrow{PT}$