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Vector Basics: Vectors, Scalars, Addition, and Scalar Multiplication

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First published at 22:23 UTC on June 25th, 2024.

#mathematics
#science
#vectors

Math Easy Solutions

MES

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In this video I go over a quick review of the basics of vector algebra, namely the definitions of vectors vs scalars, and their addition or multiplication. A vector is a quantity that has both a magnitude and a direction (such as velocity), while a scalar just has a magnitude (such as temperature). We can add vectors by adding their components, and this is visually seen by placing one vector at the tip of another. Similarly, we can multiply a vector by a scalar by multiplying the scalar into each of the vector's components. Likewise, these basics extend to subtraction as well as vectors in 3D.

Timestamps:

- Question 1: Vector vs Scalar: 0:00
- Question 2: Vector addition: 0:39
- Solution: Adding vectors geometrically using Triangle or Parallelogram Law: 0:49
- Add vectors algebraically by adding components: 2:06
- Question 3: Multiplying vector by a scalar: 3:23
- Solution: Scalar shortens or extends a vector: 3:32
- Multiply a scalar into components of a vector: 4:04

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 .

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