Question

if \\( \overleftrightarrow { a e } \perp \overleftrightarrow { e f } \\) and \\( \overleftrightarrow { b f } \perp \overleftrightarrow { e f } \\), then \\( \overleftrightarrow { a e } ? \overleftrightarrow { 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. Although \( \overrightarrow{AE} \) and \( \overrightarrow{BF} \) are in 3 - D space (in the given prism - like figure), \( \overrightarrow{AE}\perp\overrightarrow{EF}\) and \( \overrightarrow{BF}\perp\overrightarrow{EF}\), and \( \overrightarrow{AE}\) and \( \overrightarrow{BF}\) are also coplanar (both are in the plane that is parallel to the front and back faces of the prism - like figure).

Step2: Apply the parallel line property

By the property that if two lines are perpendicular to the same line and are coplanar, then \( \overrightarrow{AE}\parallel\overrightarrow{BF}\).

Answer:

A. \( \parallel \)