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Vectors and the Geometry of Space: Vectors

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First published at 21:04 UTC on November 8th, 2022.

#mathematics
#science
#education

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In this video I go over the second section in my Vectors and the Geometry of Space calculus book chapter and this time go over Vectors. Vectors are mathematical objects that describe both magnitude and direction. These are very useful in physics and science in general as it can simplify the mathematical description of 3D-dimensional space. I go over an introduction on Vectors as well as their properties and corresponding vector algebra.

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

- Introduction: 0:00
- Sections in Calculus Book Chapter: 0:58
- Topics to Cover: 2:16
1. Vectors: 3:01
2. Combining Vectors: 5:46
- Definition of Vector Addition: 7:03
- Triangle Law: 7:54
- Parallelogram Law: 8:40
- Example 1: 11:21
- Definition of Scalar Multiplication: 14:50
- Example 2: 21:01
3. Components: 22:27
- Equation 1: 35:36
- Example 3: 36:11
- Magnitude or Length of a Vector: 37:48
- Vector Algebra: 39:42
- Example 4: 50:08
- Note on n-Dimensional Vectors: 56:31
- Properties of Vectors: 58:57
- Standard Basis Vectors: 1:08:20
- Example 5: 1:20:56
- Historical Note: 1:25:04
- Unit Vectors: 1:27:15
- Example 6: 1:31:44
4. Applications: 1:35:00
- Example 7: 1:35:45