Name: Vertical and Horizontal Planes
Uploaded: 2023-05-18T17:46:35+00:00
Duration: 10 min 3 s
Description: In this video I go over graphing vertical and horizontal planes in 3D space. I start off with an example on plotting the equations z = 3 and y = 5. The first equation, z = 3, is just a horizontal plan

2 years ago

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vertical planes horizontal planes 3D space geometry vectors three-dimensional space 3D surfaces graphing in 3D mathematics science stem

In this video I go over graphing vertical and horizontal planes in 3D space. I start off with an example on plotting the equations z = 3 and y = 5. The first equation, z = 3, is just a horizontal plane in three-dimensional space and represents all the points on a surface where the z-coordinate is equal to 3. Similarly, the equation y = 5 is the set of all points where the y-coordinate is equal to 5, and which represents a vertical plane. Note that it is important to consider the context in which we are asked to plot these equations. Because if the context was graphing in 2D space, then the equation y = 5 is just a horizontal line. In general: the equation x = k is a vertical plane in the yz-plane, y = k is a vertical plane in the xz-plane, and z = k is a horizontal plane in the xy-plane.

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

- Example 1a: Horizontal Plane: 0:00
- Example 1b: Vertical Plane: 2:29
- Note on Context: 4:29
- Equations of Vertical or Horizontal Planes: 5:30

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