Straight Line and Plane - Analytic Geometry and Vectors - University Mathematics Handbook

University Mathematics Handbook (2015)

III. Analytic Geometry and Vectors

Chapter 7. Straight Line and Plane

7.1  Mutual Position of Straight Line and Plane

Let there be straight line such that and plane such that . Let be the direction vector of the line, and the normal to the plane. Therefore:

a.  The straight line is parallel to the plane if, and only if, , or

b.  The straight line is perpendicular to the plane if, and only if, , or

c.  The angle between the straight line the plane is angle between the straight line and its projection on the plane (see next Figure).

7.2  Intersection Point of a Straight Line and a Plane

To find the intersection point, we should write the straight line equation in its parametric form

(*) .

By substitution in the plane equation, we get an equation related to

.

By extracting , denoting it with (*), we obtain the intersection point.