Question

in the cube shown below, which lines are skew? ae and cg, bf and ef, ef and gh, bc and ad

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each pair

• For $\overrightarrow{AE}$ and $\overrightarrow{CG}$: They are parallel as they have the same direction in the cube.
• For $\overrightarrow{BF}$ and $\overrightarrow{EF}$: They intersect at point $F$.
• For $\overrightarrow{EF}$ and $\overrightarrow{GH}$: They are parallel.
• For $\overrightarrow{BC}$ and $\overrightarrow{DH}$: They are non - parallel and non - intersecting. They are in different non - parallel planes of the cube.

Answer:

$\overrightarrow{BC}$ and $\overrightarrow{DH}$