Question

in the square pyramid shown below, which lines are skew? (overrightarrow{fg}) and (overrightarrow{fi}) (overrightarrow{gj}) and (overrightarrow{gh}) (overrightarrow{ij}) and (overrightarrow{gh}) (overrightarrow{gj}) and (overrightarrow{fi})

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each option

• $\overleftrightarrow{FG}$ and $\overleftrightarrow{FI}$ intersect at point $F$, so they are not skew.
• $\overleftrightarrow{GJ}$ and $\overleftrightarrow{GH}$ are in the same face (the base square in this case) and intersect at point $G$, so they are not skew.
• $\overleftrightarrow{IJ}$ and $\overleftrightarrow{GH}$ are parallel (assuming $GHIJ$ is a square base), so they are not skew.
• $\overleftrightarrow{GJ}$ and $\overleftrightarrow{FI}$ are non - parallel and do not intersect as one is on the base and the other is an edge connecting the apex to a base vertex. They are skew.

Answer:

$\overleftrightarrow{GJ}$ and $\overleftrightarrow{FI}$