Properties of Vectors

In this video I go over a list of 8 properties of vectors in terms of addition and scalar multiplication. I also provide algebraic proofs for properties 1 and 2. The remaining properties, however, are fairly straightforward and so I only briefly go over them. Property 1, a + b = b + a, be seen from the Parallelogram Law and Property 2 (called the associative law), a + (b + c) = (a + b) + c, can be proved by repeated use of the Triangle Law.

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

• List of 8 Vector Properties: 0:00
• Proof of Property 1: 1:39
• Proof of Property 2: 4:32
• Other Properties: 8:55

This video was taken from my earlier video listed below:

• Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc
• Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw

Related videos:

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

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