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Equation of a Plane: Derivation Using the Dot Product

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First published at 16:26 UTC on March 19th, 2023.

#mathematics
#science
#vectors

Math Easy Solutions

MES

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In this video I go over the equation of a plane and derive it by using the Dot Product. A plane is a flat set of points in 3D. If we draw a vector parallel to it and another vector perpendicular (or normal) to the plane, then the resulting dot product of these 2 vectors must equal 0. This can then be used to derive the equation of a plane. I write the equation in 2 forms, a longer one and a shortened one that replaces the constants with the term "d".

This video was taken from my earlier video listed below:

- Discovery Project: The Geometry of a Tetrahedron: https://youtu.be/yRws7Jk2iHU
- Video notes: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T

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