What is the intersection of a plane and a line perpendicular to the plane?
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In analytic geometry,the intersection of a line and a plane in three-dimensional space can be the empty set ,a point ,or a line.It is the entire line if that line is embedded in the plane,and is the empty set if the line is parallel to the plane but outside. You may be tempted to think of planes as vehicles to be found up in the sky or at the airport. Well, rest assured, geometry is no fly‐by‐night operation. Parallel planes Parallel planes are two planes that do not intersect. In Figure 1, plane P // plane Q.  Figure 1 Parallel planes Theorem 11: If each of two planes is parallel to a third plane, then the two planes are parallel to each other (Figure 2). Figure 2 Two planes parallel to a third plane Perpendicular planes A line l is perpendicular to plane A if l is perpendicular to all of the lines in plane A that intersect l. (Think of a stick standing straight up on a level surface. The stick is perpendicular to all of the lines drawn on the table that pass through the point where the stick is standing). A plane B is perpendicular to a plane A if plane B contains a line that is perpendicular to plane A. (Think of a book balanced upright on a level surface.) See Figure 3. Figure 3 Perpendicular planes Theorem 12: If two planes are perpendicular to the same plane, then the two planes either intersect or are parallel. What is the intersection of perpendicular lines?Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
What is the intersection of plane and line Y?The intersection of a line and a plane is a point that satisfies both equations of the line and a plane. It is also possible for the line to lie along the plane and when that happens, the line is parallel to the plane.
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