Question

in the triangular prism 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 \(\overrightarrow{QR}\) and \(\overrightarrow{OP}\)

\(\overrightarrow{QR}\) and \(\overrightarrow{OP}\) are parallel as they are opposite sides of a parallelogram - like face of the prism, so they are not skew.

Step3: Analyze \(\overrightarrow{OP}\) and \(\overrightarrow{NQ}\)

\(\overrightarrow{OP}\) and \(\overrightarrow{NQ}\) are non - parallel and do not intersect. They are in different non - parallel planes, so they are skew.

Step4: Analyze \(\overrightarrow{RS}\) and \(\overrightarrow{NP}\)

\(\overrightarrow{RS}\) and \(\overrightarrow{NP}\) are non - parallel and do not intersect. They are in different non - parallel planes, so they are skew.

Step5: Analyze \(\overrightarrow{RS}\) and \(\overrightarrow{NO}\)

\(\overrightarrow{RS}\) and \(\overrightarrow{NO}\) are parallel as they are opposite sides of a parallelogram - like face of the prism, so they are not skew.

Answer:

\(\overrightarrow{OP}\) and \(\overrightarrow{NQ}\), \(\overrightarrow{RS}\) and \(\overrightarrow{NP}\)