Question

in the triangular prism shown below, which lines are skew? select all that apply.
$overrightarrow{mp}$ and $overrightarrow{nq}$ $overrightarrow{qr}$ and $overrightarrow{mo}$ $overrightarrow{or}$ and $overrightarrow{mo}$ $overrightarrow{pr}$ and $overrightarrow{mn}$

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze $\overrightarrow{MP}$ and $\overrightarrow{NQ}$

$\overrightarrow{MP}$ and $\overrightarrow{NQ}$ are in different planes and do not intersect and are not parallel.

Step3: Analyze $\overrightarrow{QR}$ and $\overrightarrow{MO}$

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

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

$\overrightarrow{OR}$ and $\overrightarrow{MO}$ intersect at point $O$, so they are not skew.

Step5: Analyze $\overrightarrow{PR}$ and $\overrightarrow{MN}$

$\overrightarrow{PR}$ and $\overrightarrow{MN}$ are in different planes, do not intersect and are not parallel.

Answer:

$\overrightarrow{MP}$ and $\overrightarrow{NQ}$, $\overrightarrow{QR}$ and $\overrightarrow{MO}$, $\overrightarrow{PR}$ and $\overrightarrow{MN}$