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

about 1 year ago

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: