Question

in the cube shown below, which lines are skew? qr and kl mq and op nr and lp qr and op

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze $\overrightarrow{QR}$ and $\overrightarrow{KL}$

$\overrightarrow{QR}$ and $\overrightarrow{KL}$ are parallel as they are opposite edges of the cube, so they are not skew.

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

$\overrightarrow{MQ}$ and $\overrightarrow{OP}$ are parallel as they are opposite edges of the cube, so they are not skew.

Step4: Analyze $\overrightarrow{NR}$ and $\overrightarrow{LP}$

$\overrightarrow{NR}$ and $\overrightarrow{LP}$ are non - parallel and do not intersect. They are in different planes and do not share any common points, so they are skew.

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

$\overrightarrow{QR}$ and $\overrightarrow{OP}$ are parallel as they are opposite edges of the cube, so they are not skew.

Answer:

$\overrightarrow{NR}$ and $\overrightarrow{LP}$