Intersection of Planes Forms a Line
In this video I show that two non-parallel planes form a line of intersection and show how to determine its equation. I also show the reverse procedure as well, that is, if we are given an equation of a line, then we can determine the equations of 2 planes that intersect to form this. This is readily evident when we are given the symmetric (or parametric) equations of a line. I also graph out the many equations of intersecting planes derived from a single line using the amazing GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/kttfn3pk
The timestamps of key parts of the video are listed below:
- Note 1: Two Linear Equations Can Represent a Line: 0:00
- Graphing Four Equations of Planes with GeoGebra 3D Graphing Calculator: 5:17
- Symmetric Equations of a Line = Two Planes: 6:40
- Note 2: Line of Intersection from Two Parametric Planes: 7:59
- Graphing Five Planes Intersecting to form One Line: 10:32
This video was taken from my earlier video listed below:
- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FO3u0IupqllNNkZTsffpIV
Related videos:
Vectors and the Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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▶️ 3Speak
This video was taken from my earlier video listed below:
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