Premium Only Content

Calculating Area of a Parallelogram and Volume of Parallelepiped with the Cross Product
In this video I show how the cross product can be used to determine the area of a parallelogram and the volume of a parallelepiped. The area of a parallelogram spanned by two vectors is equal to the length of their cross products. The volume of a parallelepiped spanned by 3 vectors is equal to their scalar triple product, which is the absolute value of the dot product between one of the vectors and the cross product of the other two vectors. Note that the scalar triple product can be calculated exactly as for the cross product using determinants, but instead of obtaining a perpendicular vector we sum up all the terms to obtain a number, aka a scalar.
Timestamps:
- Question 10: Parallelogram and Parallelepiped: 0:00
- Solution to (a): Area of a parallelogram: 0:14
- Solution to (b): Volume of a parallelepiped: 0:42
- Scalar triple product in determinant form: 1:41
- Memory tool for calculating 3rd order determinants: 2:46
Full video and playlists:
- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
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
-
6:00
Math Easy Solutions
4 days ago🔬#MESExperiments 50: Magnets in Repulsion Atwood Machine Drop Tests
1442 -
Dear America
2 hours agoHILLARY EXPOSED!! New Files Reveal She Was Behind It ALL!!! + Kamala Breaks Silence!!
84.5K55 -
LIVE
Badlands Media
6 hours agoBadlands Daily: Aug 1, 2025
4,117 watching -
LIVE
Matt Kohrs
10 hours agoTrump Tanks Stocks, Breaking Market News & Payday Friday || Live Trading
683 watching -
13:42
China Uncensored
12 hours agoChina's Invasion Has Begun
7.22K15 -
LIVE
Wendy Bell Radio
5 hours agoBUSTED
8,624 watching -
LIVE
JuicyJohns
2 hours ago $0.90 earned🟢#1 REBIRTH PLAYER 10.2+ KD🟢$500 GIVEAWAY SATURDAY!
113 watching -
LIVE
LFA TV
14 hours agoLFA TV ALL DAY STREAM - FRIDAY 8/1/25
4,226 watching -
4:02:39
The Bubba Army
1 day agoHulk Hogan had Leukemia? - Bubba the Love Sponge® Show | 8/01/25
84.4K3 -
18:36
DeVory Darkins
10 hours ago $6.83 earnedTrump scores MAJOR WIN with Americas youth as Biden drops HORRIBLE speech
29.5K40