Question

in the square pyramid shown below, which lines are skew? select all that apply.

Explanation:

Step1: Recall the definition of skew lines

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze \(\overrightarrow{QU}\) and \(\overrightarrow{RU}\)

\(\overrightarrow{QU}\) and \(\overrightarrow{RU}\) intersect at point \(U\), so they are not skew.

Step3: Analyze \(\overrightarrow{QR}\) and \(\overrightarrow{RS}\)

\(\overrightarrow{QR}\) and \(\overrightarrow{RS}\) intersect at point \(R\), so they are not skew.

Step4: Analyze \(\overrightarrow{QR}\) and \(\overrightarrow{SU}\)

\(\overrightarrow{QR}\) lies on the base square (a 2 - D plane) and \(\overrightarrow{SU}\) is a slant edge. They are non - parallel and non - intersecting.

Step5: Analyze \(\overrightarrow{QT}\) and \(\overrightarrow{TU}\)

\(\overrightarrow{QT}\) and \(\overrightarrow{TU}\) intersect at point \(T\), so they are not skew.

Answer:

\(\overrightarrow{QR}\) and \(\overrightarrow{SU}\)