Linear Equation of a Plane + Examples

In this video I go over the linear equation of a plane, which involves rewriting and simplifying the scalar equation of a plane. I do this by starting with the scalar equation of a plane and then collecting all like terms and replacing the constants addition with a single letter "d", thus obtaining the linear equation of a plane in the form: ax + by + cz + d = 0.

I also do 2 examples on planes to illustrate this concept. The first example involves finding the equation of a plane when given 3 points on the plane. The second example involves finding the point of intersection of a line and plane, whose equations are both given. And as always, I graph out the results using the amazing GeoGebra 3D graphing calculator as a double check of my work. You can play around with the calculator via these links: https://www.geogebra.org/calculator/mm6t7n4q and https://www.geogebra.org/calculator/raqsvnad.

The timestamps of key parts of the video are listed below:

- Linear Equation of a Plane: 0:00
- Example 5: Determine Equation of a Plane 3:18
- Graphing Plane with GeoGebra 3D Graphing Calculator: 11:28
- Example 6: Find Point At Intersection of Line and Plane 12:46
- Graphing with GeoGebra: 17:20

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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