Question

in the triangular pyramid 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 each pair

• For $\overrightarrow{JM}$ and $\overrightarrow{LM}$: They are in the same face (triangle $JML$), so they are not skew.
• For $\overrightarrow{JM}$ and $\overrightarrow{KL}$: $\overrightarrow{JM}$ is in the face $JML$ and $\overrightarrow{KL}$ is in the face $KLM$. They are non - parallel and non - intersecting, so they are skew.
• For $\overrightarrow{JL}$ and $\overrightarrow{KM}$: $\overrightarrow{JL}$ is in the face $JML$ and $\overrightarrow{KM}$ is in the face $KLM$. They are non - parallel and non - intersecting, so they are skew.
• For $\overrightarrow{JK}$ and $\overrightarrow{JL}$: They intersect at point $J$, so they are not skew.

Answer:

$\overrightarrow{JM}$ and $\overrightarrow{KL}$, $\overrightarrow{JL}$ and $\overrightarrow{KM}$