Question

in the triangular pyramid shown below, which lines are skew? p q s r pq and ps ps and qr pq and qr pr and ps

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 \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{PS}\): They intersect at point \(P\), so they are not skew.
• For \(\overleftrightarrow{PS}\) and \(\overleftrightarrow{QR}\): They are not parallel (since their directions are different) and they do not intersect (as they lie in different non - intersecting planes).
• For \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{QR}\): They intersect at point \(Q\), so they are not skew.
• For \(\overleftrightarrow{PR}\) and \(\overleftrightarrow{PS}\): They intersect at point \(P\), so they are not skew.

Answer:

\(\overleftrightarrow{PS}\) and \(\overleftrightarrow{QR}\)