Introduction to 3D Coordinate Systems

In this video I provide an introduction to 3D or Three-Dimensional Coordinate Systems. This section is the first part of the chapter on Vectors and the Geometry of Space from my calculus book. A 3D coordinate system is typically defined with the x-, y-, and z-axes in which the direction of the z-axis is determined by the Right-Hand Rule. Visualizing 3D geometry is often easy to use by considering the analogy of a house with 8 rooms (4 on top and 4 on the bottom) and all being in contact with the center point. In the context of 3D- coordinate systems, the 8 rooms are called octants, and the center point is the origin. I illustrate this by plotting several points in 3D. And finally I describe mathematical terms for all real numbers in a rectangular 3D coordinate system, and which is referred to as a Dimensional Rectangular Coordinate System.

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

• Introduction to Vectors and the Geometry of Space: 0:00
• Three-Dimensional Coordinate Systems: 1:30
  • Right-Hand Rule: 3:08
  • Octants: 5:00
  • Point P in 3D Space: 7:16
  • Plotting Points Examples: 13:22
• Dimensional Rectangular Coordinate System: 17:57

This video was taken from my earlier video listed below:

• Vectors and the Geometry of Space: 3D Coordinate Systems: https://youtu.be/xJ-qPJFf2gE
• Video notes: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems
• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiAJeLMzhOsrMliibfce5m

Related videos:

Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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