Question

think of each segment in the diagram as part of a line. all the angles are right angles. which line(s) contain(s) point b and appear to be skew to \\( \overleftrightarrow { c d } \\)?

Explanation:

Step1: Recall the definition of skew lines

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

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

\(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) are parallel (since all angles are right angles, in the top - front and top - back rectangles, \(AB\parallel CD\)), so they are not skew.

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

\(\overleftrightarrow{AE}\) and \(\overleftrightarrow{CD}\): \(\overleftrightarrow{AE}\) is vertical (assuming the standard orientation of the rectangular prism) and \(\overleftrightarrow{CD}\) is horizontal (in the top - back face). They do not intersect and are not parallel. Also, \(\overleftrightarrow{AE}\) contains point \(B\) (since \(A\) and \(B\) are endpoints of a vertical edge in the front - top face).

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

\(\overleftrightarrow{BC}\) and \(\overleftrightarrow{CD}\) intersect at point \(C\), so they are not skew.

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

\(\overleftrightarrow{BF}\) and \(\overleftrightarrow{CD}\): \(\overleftrightarrow{BF}\) is in the front - bottom face (assuming the standard orientation of the rectangular prism) and \(\overleftrightarrow{CD}\) is in the top - back face. They do not intersect and are not parallel. Also, \(\overleftrightarrow{BF}\) contains point \(B\).

Answer:

\(\overleftrightarrow{AE}\), \(\overleftrightarrow{BF}\)