Question

in the cube shown below, which lines are skew? submit

Explanation:

Step1: Recall the definition of skew lines

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

Step2: Analyze each pair

• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{MN}$: They intersect at point \(N\), so they are not skew.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{OG}$: In a cube, \(NR\parallel OG\) (since opposite edges of a cube are parallel), so they are not skew.
• For $\overleftrightarrow{QT}$ and $\overleftrightarrow{MP}$:
• They are not parallel.
• They do not intersect.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{PT}$: They are parallel (as \(NR\parallel PT\) in the cube), so they are not skew.

Answer:

\(\overleftrightarrow{QT}\) and \(\overleftrightarrow{MP}\)