Question

in the rectangular prism shown below, which lines are skew?
lo and no
mn and no
hi and jk
hl and jk

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 \(\overleftrightarrow{LO}\) and \(\overleftrightarrow{NO}\): They intersect at point \(O\), so they are not skew.
• For \(\overleftrightarrow{MN}\) and \(\overleftrightarrow{NO}\): They intersect at point \(N\), so they are not skew.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{JK}\):
• \(\overleftrightarrow{HI}\) is on the bottom - front face and \(\overleftrightarrow{JK}\) is on the back - right face.
• They are not parallel (their direction vectors are different) and they do not intersect (since they are on different non - intersecting planes).
• For \(\overleftrightarrow{HL}\) and \(\overleftrightarrow{JK}\): \(\overleftrightarrow{HL}\parallel\overleftrightarrow{JK}\) (as in a rectangular prism, opposite edges are parallel), so they are not skew.

Answer:

\(\overleftrightarrow{HI}\) and \(\overleftrightarrow{JK}\)