The Length of a Cross Product: Proof

In this video I go over the theorem for the length of a cross product as well as provide the proof for it. The length of a cross product is given by |a x b| = |a| |b| sin θ. I prove this by first applying the vector distance formula and then doing some next level algebra to simplify the resulting equation. Next I notice that some of the terms correspond to the Dot Product which in turn correspond to trigonometric functions, and ultimately to the desired cross product length theorem. This is an extensive proof but well worth to follow along to understand how the theorem is derived.

This video was taken from my earlier video listed below:

• Vectors and the Geometry of Space: The Cross Product:
• Video notes: @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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