Question

in the rectangular prism shown below, which lines are skew? (overrightarrow{ij}) and (overrightarrow{fg}) (overrightarrow{ij}) and (overrightarrow{ei}) (overrightarrow{ij}) and (overrightarrow{ef}) (overrightarrow{il}) and (overrightarrow{eh})

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each option

• For $\overleftrightarrow{IJ}$ and $\overleftrightarrow{FG}$: $\overleftrightarrow{IJ}$ and $\overleftrightarrow{FG}$ are parallel, so they are not skew.
• For $\overleftrightarrow{IJ}$ and $\overleftrightarrow{EI}$: $\overleftrightarrow{IJ}$ and $\overleftrightarrow{EI}$ intersect at point $I$, so they are not skew.
• For $\overleftrightarrow{IJ}$ and $\overleftrightarrow{EF}$: $\overleftrightarrow{IJ}$ and $\overleftrightarrow{EF}$ are non - parallel and non - intersecting. They are in different non - parallel planes.
• For $\overleftrightarrow{IL}$ and $\overleftrightarrow{EH}$: $\overleftrightarrow{IL}$ and $\overleftrightarrow{EH}$ are parallel, so they are not skew.

Answer:

$\overleftrightarrow{IJ}$ and $\overleftrightarrow{EF}$