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Lesson 35 – Intersection of 3 Planes

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

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Lesson 35 – Intersection of 3 Planes

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  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

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