Question

in the triangular prism shown below, which lines are skew? select all that apply. ij and mn, ij and ln, il and jk, ik and mn

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each pair

• For $\overrightarrow{IJ}$ and $\overrightarrow{MN}$: They are in different planes and do not intersect and are not parallel.
• For $\overrightarrow{IJ}$ and $\overrightarrow{LN}$: They are in different planes and do not intersect and are not parallel.
• For $\overrightarrow{IL}$ and $\overrightarrow{JK}$: $\overrightarrow{IL}$ and $\overrightarrow{JK}$ are in the same plane (the lateral face of the prism), so they are not skew.
• For $\overrightarrow{IK}$ and $\overrightarrow{MN}$: They are in different planes and do not intersect and are not parallel.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{MN}$, $\overrightarrow{IJ}$ and $\overrightarrow{LN}$, $\overrightarrow{IK}$ and $\overrightarrow{MN}$