The Dot Product: Vector and Scalar Projections

In this video I go over how the dot product is used in the vector and scalar projections of a vector onto another. The projection of one vector onto another is simply the cosine component of one vector onto another. Since we are dealing with cosines, we can write these projections to include the dot product. The vector projection is just the scalar projection multiplied by a unit vector in the direction of the vector that is being projected onto. I also go over an example on calculating both the scalar and vector projections of one vector onto another.

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

- Vector Projections: 0:00
- Scalar Projections: 3:26
- Summary of Projections: 8:54
- Example 6: 11:50

This video was taken from my earlier video listed below:

- Vectors and the Geometry of Space: The Dot Product: https://youtu.be/9uqtIk5iHys
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GbHgvpTY1mx61nTNO-Msl8

Related Videos:

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

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