Question

in the cube shown below, which lines are skew? fi and gh hi and be hi and fi bc and fg

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each option

• For $\overrightarrow{FI}$ and $\overrightarrow{GH}$: $\overrightarrow{FI}$ and $\overrightarrow{GH}$ are parallel. They lie in parallel planes and do not intersect.
• For $\overrightarrow{HI}$ and $\overrightarrow{BE}$: $\overrightarrow{HI}$ and $\overrightarrow{BE}$ are skew. They are not in the same plane, not parallel, and do not intersect.
• For $\overrightarrow{HI}$ and $\overrightarrow{FI}$: $\overrightarrow{HI}$ and $\overrightarrow{FI}$ intersect at point $I$.
• For $\overrightarrow{BC}$ and $\overrightarrow{FG}$: $\overrightarrow{BC}$ and $\overrightarrow{FG}$ are parallel. They lie in parallel planes and do not intersect.

Answer:

$\overrightarrow{HI}$ and $\overrightarrow{BE}$