Question

in the triangular prism shown below, which lines are skew?

Explanation:

Step1: Recall the definition of skew lines

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

Step2: Analyze each pair

• For \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{NQ}\): They intersect at point \(Q\), so they are not skew.
• For \(\overleftrightarrow{NO}\) and \(\overleftrightarrow{OP}\): They intersect at point \(O\), so they are not skew.
• For \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{NO}\): \(\overleftrightarrow{QS}\) is in the bottom - base plane and \(\overleftrightarrow{NO}\) is in the top - face plane. They are non - parallel and non - intersecting.
• For \(\overleftrightarrow{NP}\) and \(\overleftrightarrow{OP}\): They are in the same top - face plane. If extended, they may intersect (depending on the prism's shape, but in a prism, in the top - face quadrilateral \(NOP\) (assuming it's a planar face), they are either intersecting or parallel. In a triangular prism, \(NOP\) is a triangle - like face (in 3 - D, but in the top - face plane of the prism), and they are intersecting at \(P\) (if we consider the lines formed by the edges).

Answer:

\(\overleftrightarrow{QS}\) and \(\overleftrightarrow{NO}\)