The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


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.

10_vectors-182.gif 10_vectors-183.gif
(a) Parallel planes (b) A line L parallel lo a plane p
10_vectors-184.gif 10_vectors-185.gif
(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


Last Update: 2006-11-05