Question

1. choose the correct answer.

given \\( \overleftrightarrow { q r }, \overleftrightarrow { s t }, \overleftrightarrow { n r }, \overleftrightarrow { m q } \\), which line is skew to \\( \overleftrightarrow { q t } \\)?
\\( \overleftrightarrow { m q } \\)
\\( \overleftrightarrow { q r } \\)
\\( \overleftrightarrow { s t } \\)
\\( \overleftrightarrow { n r } \\)

Explanation:

Step1: Recall the definition of skew lines

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

Step2: Analyze \(\overleftrightarrow{QR}\)

\(\overleftrightarrow{QR}\) and \(\overleftrightarrow{QT}\) intersect at point \(Q\), so they are not skew.

Step3: Analyze \(\overleftrightarrow{ST}\)

\(\overleftrightarrow{ST}\) and \(\overleftrightarrow{QT}\) are parallel (in a cube, if two lines are in parallel planes and have the same direction, they are parallel). So they are not skew.

Step4: Analyze \(\overleftrightarrow{NR}\)

\(\overleftrightarrow{NR}\) and \(\overleftrightarrow{QT}\) are non - parallel and non - intersecting.

Step5: Analyze \(\overleftrightarrow{MQ}\)

\(\overleftrightarrow{MQ}\) and \(\overleftrightarrow{QT}\) are perpendicular (intersect at \(Q\)), so they are not skew.

Answer:

\(\overleftrightarrow{NR}\)