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 rs? select two options.

Explanation:

Step1: Recall the property of perpendicular lines

If a line is perpendicular to a plane, then any line in that plane perpendicular to the projection of the first - line onto the plane is perpendicular to the first line. Since planes \(X\) and \(Y\) are perpendicular, and lines \(EA\) and \(FG\) are parallel.

Step2: Analyze each vector

• For \(\overrightarrow{EA}\): Given that \(EA\) is parallel to \(FG\). If we consider the relationship between the planes \(X\) and \(Y\) (perpendicular), and the fact that \(RS\) is the intersection line of the two planes. If a line in plane \(X\) (where \(EA\) is related to points in plane \(X\)) and the intersection line \(RS\) of two perpendicular planes \(X\) and \(Y\), we know that if a line in one of the two perpendicular planes is parallel to a line in the other plane's relevant direction (based on the perpendicular - plane and line - parallel relationships), \(\overrightarrow{EA}\) can be perpendicular to \(\overrightarrow{RS}\).
• For \(\overrightarrow{FG}\): Since \(EA\parallel FG\), if \(\overrightarrow{EA}\perp\overrightarrow{RS}\), then \(\overrightarrow{FG}\perp\overrightarrow{RS}\) (because if \(a\parallel b\) and \(a\perp c\), then \(b\perp c\))

Answer:

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