In this video I show that the dot product and cross product have a basic arithmetic multiplication property when multiplied by a scalar. That is, the scalar can be multiplied either after the dot and cross products are calculated, or multiplied inside either vector before taking the dot / cross products. Both scenarios yield the same result!
Time stamps:
- Question 8: Multiplying scalar inside a dot product: 0:00
- Proof for 2D dot product case: 1:15
- Question 9: Multiplying scalar inside a cross product: 3:45
- Proof of scalar distribution property: 5:08
Full video and playlists:
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiYS2qR98dzUjsx-0PRPbC
- Notes: https://peakd.com/hive-128780/@mes/vectors-geometry-true-false-quiz
- Vectors and the Geometry of Space: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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