Question

in the cube shown below, which lines are skew? tx and uy rv and vw rs and tu tu and vy

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze option 1

$\overleftrightarrow{TX}$ and $\overleftrightarrow{UY}$ are non - parallel and do not intersect. They are in different planes.

Step3: Analyze option 2

$\overleftrightarrow{RV}$ and $\overleftrightarrow{VW}$ intersect at point $V$, so they are not skew.

Step4: Analyze option 3

$\overleftrightarrow{RS}$ and $\overleftrightarrow{TU}$ are parallel, so they are not skew.

Step5: Analyze option 4

$\overleftrightarrow{TU}$ and $\overleftrightarrow{VY}$ are in the same plane (the front - left face of the cube), so they are not skew.

Answer:

$\overleftrightarrow{TX}$ and $\overleftrightarrow{UY}$