Lines and Planes

Two planes are said to be parallel if their normal vectors are parallel.

A line L is said to be parallel to a plane p if the direction vectors of L are perpendicular to the normal vectors of p.

Two planes are said to be perpendicular if their normal vectors are perpendicular.

A line L is said to be perpendicular to a plane p if the direction vectors of L are normal to p.

Figure 10.5.9 illustrates these definitions.

(a) Parallel planes	(b) A line L parallel lo a plane p
(c) Perpendicular planes	(d) A line L perpendicular to a plane p
Figure 10.5.9

Example 8: Plane and Line Parallel?

Example 9: Line Perpendicular to a Plane

Example 10: Plane Containing a Line Perpendicular to Another Plane

A line which is not parallel to a plane will intersect the plane at exactly one point.

Example 11: Intersection Point Between a Line and a Plane

Two planes which are not parallel intersect at a line.

Example 12: Intersection Lines Between Planes