Geometry of a Tetrahedron: Question 2: Volume of a Tetrahedron in Vector Coordinate Form

In this video I go over Question 2 of the Discovery Project: Geometry of a Tetrahedron. This question involves determining the volume of a tetrahedron but in vector coordinate form. The formula of the volume of a tetrahedron is V = 1/3·A·h. To get this formula in vector coordinate form, we can determine the area A of the triangular base as being half the cross product. For the height h, we first have to determine the equation of the plane that contains the area A and then calculate the distance from the opposite vertex to the plane. After going over the equation of a plane and the equation for the distance from a point to the plane, we can thus calculate the volume of a tetrahedron for any set of coordinates. I also graph the tetrahedron using the amazing GeoGebra 3D graphing calculator which also calculates its volume as well which I use as a double check.

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

• Question 2: 0:00
• Solution to Part (a): 1:11
  • The Equation of a Plane: 6:21
  • The Distance from a Point to a Plane: 10:33
• Solution to Part (b): 17:31
  • Graphing 3D Tetrahedron in GeoGebra: 29:06

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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