Discovery Project: The Geometry of a Tetrahedron

8 months ago

In this video I go over the Discovery Project titled The Geometry of a Tetrahedron. Discovery Projects are advanced math problems in each chapter of my calculus book, and this one is part of the Vectors and Geometry of Space chapter. This project involves 3 Questions regarding the tetrahedron, which is a triangular pyramid. The first question involves finding the areas of each triangular face using the Cross Product. The second question involves finding the volume of a tetrahedron when written in coordinate vector form. And the third question involves deriving the 3D version of the Pythagorean Theorem, which is: the 3 triangular areas squared at a vertex sum up to equal the square of the opposite triangular area!

The topics covered as well as their timestamps are listed below.

- Introduction: 0:00
- Calculus Book Reference: 0:56
- Sections in Calculus Book Chapter: 1:12
- Topics to Cover: 2:03
1. Discovery Project: The Geometry of a Tetrahedron: 2:25
2. 3 Questions: 3:05
- Question 1: 5:00
- Question 2: 34:59
- Solution to Part (a): 36:10
- The Equation of a Plane: 41:20
- The Distance from a Point to a Plane: 45:31
- Solution to Part (b): 52:43
- Question 3: 1:05:35

Download video notes:!As32ynv0LoaIicNsAiLSiBI1ivS39w?e=V33CkF

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View video sections playlist:

View the full Vectors and the Geometry of Space series:

Related Videos:

The Cross Product:

The Dot Product:

Complex Numbers as Rotation Matrices:


3D Coordinate Systems: .



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