1 / 23

Understanding Intersection of 3 Planes Concepts | Geometry Lesson

Learn to recognize geometric intersections of three planes and solve for points and lines of intersection using system of equations. Practice different cases for thorough understanding.

rosenj
Download Presentation

Understanding Intersection of 3 Planes Concepts | Geometry Lesson

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 35 – Intersection of 3 Planes September 17, 2013 Fernando Morales

  2. Learning Goals • Recognize geometrically intersection three planes • Solve for the point and/or line of intersection of three planes • Able to use the iPad app to verify solutions

  3. Cases with One or More Points of Intersection of 3 Planes • There is just one solution to the corresponding system of equations. • This is a single point. The coordinates of the point of intersection will satisfy each of the three equations.

  4. Cases with One or More Points of Intersection of 3 Planes • There are an infinite number of solutions to the related system of equations. Geometrically, this corresponds to a lie, and the solution is given in terms of one parameter. • The tree planes intersect along a lie and are mutually non-coincident.

  5. Cases with One or More Points of Intersection of 3 Planes • There are an infinite number of solutions to the related system of equations. Geometrically, this corresponds to a lie, and the solution is given in terms of one parameter. • The two planes are coincident, and the third plane cuts through these two planes intersecting along a line.

  6. Cases with One or More Points of Intersection of 3 Planes • Three planes are coincident, and there are an infinite number of solutions to the related system of equations. The number of solutions corresponds to the infinite number of points on a plane and the solution is given in terms of two parameters. • In this case, there are three coincident planes that have identical equations or can be reduced to three equivalent equations.

  7. Cases with No Points of Intersections of 3 Planes Three planes form a triangular prism as shown. This means that, if you consider any two of the three planes, they intersect in a line and each of these three lines is parallel to the others.

  8. Cases with No Points of Intersections of 3 Planes Each of the parallel planes has a line of intersection with the third plane, But there is no intersection between all three planes.

  9. Cases with No Points of Intersections of 3 Planes • All three planes do not have any points of intersection.

  10. Cases with No Points of Intersections of 3 Planes • All three planes do not have any points of intersection.

  11. Required Before Next Class • Chapter 8 Review # 1, 2, 3, 4, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23 • Chapter 8 Practice Test # 1-14, 16, 17, 21, 22, 23

More Related