Question

in the cube shown below, which lines are skew?
options: (overleftrightarrow{qt}) and (overleftrightarrow{mp}), (overleftrightarrow{mn}) and (overleftrightarrow{mq}), (overleftrightarrow{nr}) and (overleftrightarrow{no}), (overleftrightarrow{st}) and (overleftrightarrow{mq})

Explanation:

Step1: Define skew lines

Skew lines are non-parallel, non-intersecting, and not coplanar.

Step2: Analyze each option

• $\overline{QT}$ & $\overline{MP}$: Parallel (same direction in cube).
• $\overline{MN}$ & $\overline{MQ}$: Intersect at $M$.
• $\overline{NR}$ & $\overline{NO}$: Intersect at $N$.
• $\overline{ST}$ & $\overline{MQ}$: Non-parallel, non-intersecting, not coplanar.

Answer:

D. $\overline{ST}$ and $\overline{MQ}$