This lesson covers the equations for a line and a plane in three dimensions. It introduces the parametric equations for a line as well as the symmetric equations obtained by eliminating the parameter. The linear equation for a plane is also introduced. Finally, there are several problems that ask students to apply geometrical reasoning to find intersections of lines and planes. Vectors are not used in this lesson.
This lesson is meant for a Multivariable Calculus course, but it could be used in Geometry as part of a unit on three-dimensional geometry. No calculus is introduced in this lesson. Another option is to use it after AP Calculus exams have finished.
Detailed answer keys are included.
The topics covered include:
-Parametric Equations for a Line in Two Dimensions
-Parametric Equations for a Line in Three Dimensions
-Symmetric Equations of a Line
-Linear Equation of a Plane
-Finding the Linear Equation of a Plane
-Finding the Intersection of a Line and a Plane
-Finding the Intersection of Two Planes
In this product, you will find the following:
-Powerpoint Presentation (26 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)
This lesson is part of a larger unit on The Geometry of Space. The complete unit includes the following:
-Working in Three Dimensions
-Spheres and Cylindrical Surfaces
-Lines and Planes
-Quadric Surfaces (coming soon!)
-Cylindrical Coordinates (coming soon!)
-Spherical Coordinates (coming soon!)