Question

in the rectangular prism shown below, which lines are skew?
jn and kn
ij and im
ij and kn
mn and gh
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Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each option

• For $\overrightarrow{JN}$ and $\overrightarrow{KN}$, they intersect at point $N$, so they are not skew.
• For $\overrightarrow{IJ}$ and $\overrightarrow{IM}$, they are in the same face (the top - right face) and intersect at point $I$, so they are not skew.
• For $\overrightarrow{IJ}$ and $\overrightarrow{KN}$, they are non - parallel and do not intersect. $\overrightarrow{IJ}$ is in the top - right face and $\overrightarrow{KN}$ is in a non - parallel face.
• For $\overrightarrow{MN}$ and $\overrightarrow{GH}$, they are parallel (both are horizontal edges in parallel faces), so they are not skew.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{KN}$