# Vectors and the Geometry of Space: The Cross Product

4

• 26
• 0
• 0.906

• Published on Jan 30, 2023

In this video I go over further into Vectors and the Geometry of Space and this time cover the Cross Product. The cross product is a very useful concept and is defined such that it produces a vector that is perpendicular to 2 other vectors. This property is very useful in physics, especially when dealing with rotation and torque.

While the definition of the cross product involves a lot of algebra, I show that it can be made easier to both remember and calculate by writing it in determinant form. Furthermore, I show that the length of the cross product is equal to the parallelogram formed from 2 vectors. I also go over several other theorems and topics that follow from the cross product, such as the right-hand rule, the scalar triple product, and a number of properties of the cross product. This is a great in-depth introduction and examination of the cross product so make sure to watch this whole video!

The topics covered as well as their timestamps are listed below.

• Introduction: 0:00
• Calculus Book Reference: 0:44
• Sections in Calculus Book Chapter: 1:06
• Topics to Cover: 1:38
1. The Cross Product: 3:01
• Definition: 15:36
• Historical Note: Sir William Rowan Hamilton: 16:55
2. Determinants: 18:01
• Cross Product in Determinant Form: 24:48
• Example 1: 30:27
• Example 2: 33:38
3. Cross Product Orthogonality Proof: 36:50
• Theorem 1: 37:19
4. Right-Hand Rule: 43:07
5. Cross Product Length: 44:58
• Theorem 2: 45:23
6. Corollary: 1:11:47
7. Geometric Interpretation of Theorem 2: 1:15:19
• Example 3: 1:19:46
• Example 4: 1:31:44
8. Properties of the Cross Product: 1:35:03
• Theorem 3: 1:45:36
• Proof of Property 5: 1:47:33
9. Triple Products: 1:53:09
• Formula of a Parallelepiped: 2:01:08
• Example 5: 2:02:05
10. Torque: 2:07:00
• Example 6: 2:10:31
11. Exercises: 2:14:42
• Exercise 1: 2:15:20
• Exercise 2: 2:18:23
• Exercise 3: 2:22:12
• Exercise 4: 2:28:16
• Exercise 5: Vector Triple Product: 2:34:08

View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product

Related Videos:

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

Vectors and the Geometry of Space: The Dot Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product

Complex Numbers as Rotation Matrices: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices

3D Coordinate Systems: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems .

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

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

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
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

###### Tags :

To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

01:00:35
19 views 3 years ago \$
28:14
2 views 3 years ago \$
04:20
5 views a year ago \$
01:29
12 views 8 months ago \$
56:03
41 views a year ago \$

#### More Videos

04:12
5 views a year ago \$
03:37
16 views 3 months ago \$
01:34
19 views 2 years ago \$
02:28
12 views 4 years ago \$
12:49
03:18
18 views 10 months ago \$
09:53
2 views 4 years ago \$
01:49
7 views a month ago \$
15:00
1 views 9 months ago \$
12:13
01:00
25 views 4 years ago \$
07:59
2 views 4 years ago \$
03:08
3 views 2 years ago \$
01:14
0 views 2 years ago \$
03:16
47 views a week ago \$
00:55
2 views 3 years ago \$
15:50
49 views 3 years ago \$
01:43
5 views a year ago \$
05:34
45 views 2 years ago \$
33:13
10:19
5 views a year ago \$
15:17
5 views a year ago \$
02:54
37 views 2 years ago \$