Question

in the rectangular prism shown below, which lines are skew?
$overrightarrow{hi}$ and $overrightarrow{gh}$ $overrightarrow{bf}$ and $overrightarrow{fg}$ $overrightarrow{dh}$ and $overrightarrow{fi}$ $overrightarrow{bf}$ and $overrightarrow{ei}$

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each option

• $\overrightarrow{HI}$ and $\overrightarrow{GH}$: $\overrightarrow{HI}$ is not defined in the prism, so this option is incorrect.
• $\overrightarrow{BF}$ and $\overrightarrow{FG}$: $\overrightarrow{BF}$ and $\overrightarrow{FG}$ intersect at point $F$, so they are not skew.
• $\overrightarrow{DH}$ and $\overrightarrow{FI}$: $\overrightarrow{DH}$ and $\overrightarrow{FI}$ are non - parallel and do not intersect. They are in different planes and satisfy the definition of skew lines.
• $\overrightarrow{BF}$ and $\overrightarrow{EI}$: $\overrightarrow{BF}$ and $\overrightarrow{EI}$ are parallel (as they are opposite edges of a rectangular prism), so they are not skew.

Answer:

$\overrightarrow{DH}$ and $\overrightarrow{FI}$