Question

in the cube shown below, which lines are skew? select all that apply.

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each pair

• For $\overrightarrow{GK}$ and $\overrightarrow{JK}$: $\overrightarrow{GK}$ and $\overrightarrow{JK}$ intersect at point $K$, so they are not skew.
• For $\overrightarrow{FJ}$ and $\overrightarrow{HI}$: $\overrightarrow{FJ}$ and $\overrightarrow{HI}$ are non - parallel and do not intersect as they lie in different non - intersecting planes of the cube, so they are skew.
• For $\overrightarrow{DG}$ and $\overrightarrow{EF}$: $\overrightarrow{DG}$ and $\overrightarrow{EF}$ are non - parallel and do not intersect as they lie in different non - intersecting planes of the cube, so they are skew.
• For $\overrightarrow{IJ}$ and $\overrightarrow{DE}$: $\overrightarrow{IJ}$ and $\overrightarrow{DE}$ are non - parallel and do not intersect as they lie in different non - intersecting planes of the cube, so they are skew.

Answer:

$\overrightarrow{FJ}$ and $\overrightarrow{HI}$, $\overrightarrow{DG}$ and $\overrightarrow{EF}$, $\overrightarrow{IJ}$ and $\overrightarrow{DE}$