Question

if \\( \overrightarrow { a e } \perp \overrightarrow { e f } \\) and \\( \overrightarrow { b f } \perp \overrightarrow { e f } \\), then \\( \overrightarrow { a e } ? \overrightarrow { b f } \\).

Explanation:

Step1: Recall the property of lines perpendicular to the same line

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Here, \( \overrightarrow{AE}\perp\overrightarrow{EF}\) and \( \overrightarrow{BF}\perp\overrightarrow{EF}\). Although the figure is a 3 - D figure (a prism), \(AE\) and \(BF\) are in the same lateral face (the face \(ABFE\) of the prism).

Step2: Apply the property

Since \(AE\) and \(BF\) are both perpendicular to \(EF\) and lie in the same face (a plane - like structure in the prism's lateral face \(ABFE\)), by the property of lines in a plane (in the context of the lateral face which can be considered as a plane for the relationship of \(AE\), \(BF\), and \(EF\)), we can conclude that \(AE\parallel BF\).

Answer:

A. \( \parallel \)