Question

in the cube 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 $\overrightarrow{PQ}$ and $\overrightarrow{MQ}$

$\overrightarrow{PQ}$ and $\overrightarrow{MQ}$ share point $Q$, so they are not skew.

Step3: Analyze $\overrightarrow{KL}$ and $\overrightarrow{MQ}$

$\overrightarrow{KL}$ and $\overrightarrow{MQ}$ are in different planes, not parallel and do not intersect, so they are skew.

Step4: Analyze $\overrightarrow{PQ}$ and $\overrightarrow{LM}$

$\overrightarrow{PQ}$ and $\overrightarrow{LM}$ are in different planes, not parallel and do not intersect, so they are skew.

Step5: Analyze $\overrightarrow{NO}$ and $\overrightarrow{MQ}$

$\overrightarrow{NO}$ and $\overrightarrow{MQ}$ are in different planes, not parallel and do not intersect, so they are skew.

Answer:

$\overrightarrow{KL}$ and $\overrightarrow{MQ}$, $\overrightarrow{PQ}$ and $\overrightarrow{LM}$, $\overrightarrow{NO}$ and $\overrightarrow{MQ}$