Geometry of a Tetrahedron: Question 1: Calculating Area with Cross Products

In this video I go over Question 1 of the Discovery Project: Geometry of a Tetrahedron. In this question, we are asked to show that the 4 vectors pointing away from the tetrahedron and with lengths equal to the area of the opposite facing triangles all sum up to equal the 0 vector. In solving this question, I calculate the vectors as cross products, and their lengths as half the length of the cross products. However, for the direction of the resulting cross product vectors, I ensure they are indeed in the direction opposite of the triangular face, so I make the vector components positive or negative accordingly.

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

Related Videos:

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

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