The Cross Product Length is the Area of a Parallelogram + Examples

In this video I go over the geometric interpretation of the length of a cross product and show that it is indeed the area of the parallelogram formed by the two vectors a and b. I first illustrate this geometric view and then do 2 examples on it. In the first example I find a vector perpendicular to a plane spanned by 3 points, and in the second example I determine the area of this plane. Since there are 3 points, the area is just a triangle and is equal to half the parallelogram formed from the cross product length of the perpendicular vector from the first example.

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

• Geometric Characterization of Theorem 2: 0:00
• Example 3: 4:27
• Example 4: 16:24

This video was taken from my earlier video listed below:

• Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
• Video notes: https://peakd.com/hive-128780/@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 .

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes

MORE Links: https://linktr.ee/matheasy

Email me: contact@mes.fm

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps