Question

in the cube shown below, which lines are skew?

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 \(\overleftrightarrow{TX}\) and \(\overleftrightarrow{UV}\): \(\overleftrightarrow{TX}\parallel\overleftrightarrow{UV}\) (since in a cube, opposite edges are parallel), so they are not skew.
• For \(\overleftrightarrow{VW}\) and \(\overleftrightarrow{WY}\): \(\overleftrightarrow{VW}\) and \(\overleftrightarrow{WY}\) intersect at point \(W\), so they are not skew.
• For \(\overleftrightarrow{VW}\) and \(\overleftrightarrow{WX}\): \(\overleftrightarrow{VW}\) and \(\overleftrightarrow{WX}\) intersect at point \(W\), so they are not skew.
• For \(\overleftrightarrow{RS}\) and \(\overleftrightarrow{TX}\): \(\overleftrightarrow{RS}\) and \(\overleftrightarrow{TX}\) are non - parallel and non - intersecting.

Answer:

\(\overleftrightarrow{RS}\) and \(\overleftrightarrow{TX}\)