Question

in the square 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 $\overrightarrow{MP}$ and $\overrightarrow{NO}$: $\overrightarrow{MP}$ and $\overrightarrow{NO}$ are non - parallel and do not intersect as $\overrightarrow{NO}$ lies in the base square and $\overrightarrow{MP}$ is a slant edge.
• For $\overrightarrow{PQ}$ and $\overrightarrow{MO}$: $\overrightarrow{PQ}$ is a side of the base square and $\overrightarrow{MO}$ is a slant edge. They are non - parallel and do not intersect.
• For $\overrightarrow{MP}$ and $\overrightarrow{NQ}$: $\overrightarrow{MP}$ is a slant edge and $\overrightarrow{NQ}$ is a diagonal of the base square. They are non - parallel and do not intersect.
• For $\overrightarrow{MO}$ and $\overrightarrow{OP}$: $\overrightarrow{MO}$ is a slant edge and $\overrightarrow{OP}$ is a side of the base square. They are non - parallel and do not intersect.

Answer:

$\overrightarrow{MP}$ and $\overrightarrow{NO}$, $\overrightarrow{PQ}$ and $\overrightarrow{MO}$, $\overrightarrow{MP}$ and $\overrightarrow{NQ}$, $\overrightarrow{MO}$ and $\overrightarrow{OP}$