Parametric Equations of a Line

In this video I convert the vector equation of a line into its parametric equations form. To do this I first expand the vector equation by writing out its components and then summing them up. Then I equate each x, y, and z coordinate with its corresponding components resulting in 3 equations. These 3 equations are called the Parametric Equations of a line. I also go over an example on finding the vector and parametric equations of a line that passes through the point (5, 1, 3) and is parallel to the vector [1, 4, -2]. Finally, I graph the line using the amazing GeoGebra 3D graphing calculator, which you can play around with here: https://www.geogebra.org/calculator/wszwnpme

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

- Parametric Equations of a Line: 0:00
- Example 1: 4:31
- Solution to 1(a): 4:57
- Solution to 1(b): 13:03

This video was taken from my earlier video listed below:

- Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8
- Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FO3u0IupqllNNkZTsffpIV

Related videos:

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

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