Question

in the rectangular prism shown below, which lines are skew?
image of rectangular prism with vertices labeled x, w, v, u, s, r, q, t
options:
\overleftrightarrow{st} and \overleftrightarrow{wx}
\overleftrightarrow{qt} and \overleftrightarrow{rv}
\overleftrightarrow{qr} and \overleftrightarrow{rv}
\overleftrightarrow{qu} and \overleftrightarrow{uv}

Explanation:

Step1: Define skew lines

Skew lines are non-parallel, non-intersecting, and not coplanar.

Step2: Analyze Option 1 ($\overline{ST}$ & $\overline{WX}$)

$\overline{ST}$ and $\overline{WX}$ are parallel (same direction in prism), so not skew.

Step3: Analyze Option 2 ($\overline{QT}$ & $\overline{RV}$)

$\overline{QT}$ and $\overline{RV}$: no intersection, not parallel, not coplanar → skew.

Step4: Analyze Option 3 ($\overline{QR}$ & $\overline{RV}$)

$\overline{QR}$ and $\overline{RV}$ intersect at $R$, so not skew.

Step5: Analyze Option 4 ($\overline{QU}$ & $\overline{UV}$)

$\overline{QU}$ and $\overline{UV}$ intersect at $U$, so not skew.

Answer:

B. $\overline{QT}$ and $\overline{RV}$