Question

in the rectangular prism shown below, which lines are skew? fg and ei dg and fg fj and gk fj and ei

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each option

• For $\overrightarrow{FG}$ and $\overrightarrow{EI}$: $\overrightarrow{FG}$ and $\overrightarrow{EI}$ are parallel as they are opposite sides of a rectangular face.
• For $\overrightarrow{DG}$ and $\overrightarrow{FG}$: $\overrightarrow{DG}$ and $\overrightarrow{FG}$ intersect at point $G$.
• For $\overrightarrow{FJ}$ and $\overrightarrow{GK}$: $\overrightarrow{FJ}$ and $\overrightarrow{GK}$ are non - parallel and do not intersect. They are in different non - parallel planes.
• For $\overrightarrow{FJ}$ and $\overrightarrow{EI}$: $\overrightarrow{FJ}$ and $\overrightarrow{EI}$ intersect at a point (extend the lines if necessary).

Answer:

$\overrightarrow{FJ}$ and $\overrightarrow{GK}$