Question

in the rectangular prism shown below, which lines are intersecting?

Explanation:

Step1: Recall the definition of intersecting lines

Intersecting lines are lines that meet at a point.

Step2: Analyze each pair

• For \(\overleftrightarrow{QR}\) and \(\overleftrightarrow{ST}\): In a rectangular prism, \(QR\) and \(ST\) are parallel (since opposite sides of a rectangular - faced prism are parallel in such cases), so they do not intersect.
• For \(\overleftrightarrow{SV}\) and \(\overleftrightarrow{UV}\): These two lines meet at the point \(V\).
• For \(\overleftrightarrow{OS}\) and \(\overleftrightarrow{UV}\): These lines are skew (not in the same plane and do not intersect).
• For \(\overleftrightarrow{OR}\) and \(\overleftrightarrow{SV}\): These lines are skew (not in the same plane and do not intersect).

Answer:

\(\overleftrightarrow{SV}\) and \(\overleftrightarrow{UV}\)