Question

planes x and y are perpendicular. points a, e, f, and g are points only in plane x. points r and s are points in both planes x and y. lines ea and fg are parallel. based on this information, which pair of lines, together, could be perpendicular to \\( \overline{rs} \\)? select two options. \\( \square \overrightarrow{ea} \\) \\( \square \overrightarrow{er} \\) \\( \square \overrightarrow{ef} \\) \\( \square \overrightarrow{fg} \\) \\( \square \overrightarrow{fs} \\)

Explanation:

Step1: Analyze the relationship between lines and planes

Since planes \(X\) and \(Y\) are perpendicular, and \(RS\) is in plane \(Y\). Lines in plane \(X\) that are perpendicular to the intersection line of planes \(X\) and \(Y\) (which is related to \(RS\) in terms of perpendicularity due to plane - plane perpendicularity) can be perpendicular to \(RS\).

Step2: Use the parallel property

Given that \(EA\parallel FG\). If one of them is perpendicular to \(RS\), the other is also perpendicular to \(RS\) (because if a line is perpendicular to a line and another line is parallel to the first line, then the second line is also perpendicular to the original line).

Answer:

\(\overrightarrow{EA}\), \(\overrightarrow{FG}\)