Question

in the triangular prism shown below, which lines are skew? select all that apply. (overleftrightarrow{qr}) and (overleftrightarrow{mn}) (overleftrightarrow{pr}) and (overleftrightarrow{nq}) (overleftrightarrow{pq}) and (overleftrightarrow{mo}) (overleftrightarrow{or}) and (overleftrightarrow{mn})

Explanation:

To determine skew lines, we recall that skew lines are non - parallel, non - intersecting, and lie in different planes.

Step 1: Analyze \(\overleftrightarrow{QR}\) and \(\overleftrightarrow{MN}\)

• \(QR\) and \(MN\): In a triangular prism, \(QR\) and \(MN\) are parallel (since the opposite sides of the parallelogram faces of the prism are parallel). So they are not skew.

Step 2: Analyze \(\overleftrightarrow{PR}\) and \(\overleftrightarrow{NQ}\)

• \(PR\) and \(NQ\): These two lines are parallel (as they are opposite sides of a parallelogram - like face in the prism). So they are not skew.

Step 3: Analyze \(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{MO}\)

• \(PQ\) and \(MO\): \(PQ\) lies on one face of the prism and \(MO\) lies on another non - parallel face. They do not intersect and are not parallel. So they are skew.

Step 4: Analyze \(\overleftrightarrow{OR}\) and \(\overleftrightarrow{MN}\)

• \(OR\) and \(MN\): \(OR\) and \(MN\) are in different planes, they do not intersect and are not parallel. So they are skew.

Answer:

\(\overleftrightarrow{PQ}\) and \(\overleftrightarrow{MO}\), \(\overleftrightarrow{OR}\) and \(\overleftrightarrow{MN}\)