Question

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

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze $\overrightarrow{FJ}$ and $\overrightarrow{JK}$

$\overrightarrow{FJ}$ and $\overrightarrow{JK}$ are on the same face (the front - right face of the cube), so they intersect at point $J$, not skew.

Step3: Analyze $\overrightarrow{GK}$ and $\overrightarrow{IJ}$

$\overrightarrow{GK}$ is on the top - right face and $\overrightarrow{IJ}$ is on the bottom - left face. They are non - parallel and non - intersecting, so they are skew.

Step4: Analyze $\overrightarrow{IL}$ and $\overrightarrow{EF}$

$\overrightarrow{IL}$ is on the left - top face and $\overrightarrow{EF}$ is on the bottom - front face. They are non - parallel and non - intersecting, so they are skew.

Step5: Analyze $\overrightarrow{KL}$ and $\overrightarrow{EH}$

$\overrightarrow{KL}$ is on the top - left face and $\overrightarrow{EH}$ is on the bottom - front face. They are non - parallel and non - intersecting, so they are skew.

Answer:

$\overrightarrow{GK}$ and $\overrightarrow{IJ}$, $\overrightarrow{IL}$ and $\overrightarrow{EF}$, $\overrightarrow{KL}$ and $\overrightarrow{EH}$