Question

in the triangular prism shown below, which lines are skew? ac and ef ad and be de and ef ab and bc

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each option

• For $\overrightarrow{AC}$ and $\overrightarrow{EF}$: $\overrightarrow{AC}$ and $\overrightarrow{EF}$ are parallel. They lie in parallel planes (the two triangular faces of the prism) and do not intersect, so they are not skew.
• For $\overrightarrow{AD}$ and $\overrightarrow{BE}$: $\overrightarrow{AD}$ and $\overrightarrow{BE}$ are parallel. They are the lateral edges of the prism and lie in parallel planes, so they are not skew.
• For $\overrightarrow{DE}$ and $\overrightarrow{EF}$: $\overrightarrow{DE}$ and $\overrightarrow{EF}$ intersect at point $E$, so they are not skew.
• For $\overrightarrow{AB}$ and $\overrightarrow{BC}$: $\overrightarrow{AB}$ and $\overrightarrow{BC}$ are in the same plane (the base triangle $ABC$) and intersect at point $B$, so they are not skew.

Since none of the given pairs are skew, we assume there is a misunderstanding in the problem - setup. But if we consider the nature of skew lines, in a triangular prism, for example, a lateral edge and a non - parallel line in the base that does not intersect it would be skew. In a correct scenario, if we had a line in one base and a non - parallel non - intersecting line in the other base or a non - parallel non - intersecting lateral edge and a base line, those would be skew. However, based on the given options, there are no skew lines among them.

Answer:

None of the above pairs are skew.