The Cross Product: Triple Products

In this video I go over triple products, and more specifically the scalar triple product from Property 5 of my previous video. The scalar triple product can be written in determinant form and its geometric significance is that it makes up the volume of a parallelepiped, which is just a 3D parallelogram. I illustrate this triple product by an example and show that if the scalar triple product is equal to zero then all the vectors must be coplanar; that is, they are on the same plane and thus their volume is zero.

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

- Scalar Triple Product: 0:00
- Formula of a Parallelepiped: 7:59
- Example 5: 8:55

This video was taken from my earlier video listed below:

- Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FuRJ8rg-YVQvfPoPOwhuRW

Related Videos:

Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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