Geometric Interpretation of the Dot Product
In this video I go over the geometric interpretation of the dot product and show that it can be written to include the angle between the 2 vectors. That is, a ⋅ b = |a| |b| cos θ. I also derive this formula using the law of cosines, which I first went over in my earlier video. I also go over several examples, as well as a corollary on determining the angle directly from 2 vectors.
The timestamps of key parts of the video are listed below:
Geometric Interpretation: 0:00
Definition 2: 3:17
Example 2: 18:31
Corollary: 21:17
Example 3: 22:03
This video was taken from my earlier video listed below:
Vectors and the Geometry of Space: The Dot Product: • Vectors and the Geometry of Space: The Dot...
Video notes: https://peakd.com/hive-128780/@mes/ve...
Playlist: • The Dot Product
Related Videos:
Vectors and the Geometry of Space Playlist: • Vectors and the Geometry of Space .
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