In this video I go over what direction numbers and symmetric equations of a line are. Direction numbers are the components of the parallel vector in a vector equation of a line. We can use any three numbers that are proportional to the direction numbers and still get the same line. This is because the vector and parametric equations of a line are not unique.
The symmetric equations involve taking out the parameter t from each of the three parametric equations and then equating them to get equations that are symmetric, as the name implies. If one of the direction numbers is 0, then the symmetric equations can be simplified by having that coordinate equal to the corresponding point on the line.
I also go over an example on finding the parametric and symmetric equations of a line that passes through the points (2, 4, -3) and (3, -1, 1) and then determine the point it intersects the xy-plane. And as usual, I graph out the line using the amazing Desmos 3D graphing calculator: https://www.geogebra.org/calculator/cwrevexn
The timestamps of key parts of the video are listed below:
- Direction Numbers: 0:00
- Symmetric Equations of a Line: 3:40
- Symmetric Equations if a Direction Number is Zero: 7:00
- Example 2: 9:21
- Solution to 2(a): 9:46
- Solution to 2(b): 15:34
- Note on Example 2: 20:30
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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