Name: Example on Skew Lines: Lines that Aren't Parallel and Don't Intersect
Uploaded: 2023-07-18T19:39:52+00:00
Duration: 10 min 56 s
Description: In this video I go over an example on determining whether 2 lines with given parametric equations are skew lines; which are lines that do not intersect and are not parallel. By looking at the directio

2 years ago

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skew lines vectors vector algebra parametric equations of a line direction vector direction numbers parallel vectors point of intersection geogebra 3d coordinates vector equation of a line

In this video I go over an example on determining whether 2 lines with given parametric equations are skew lines; which are lines that do not intersect and are not parallel. By looking at the direction vectors of each line, I note that the given lines are not parallel because their vector components are not scalar multiples of each other (aka they are not proportional). If the lines are not skew then they would have a point of intersection, in which case there would then exist a point (x, y, z) that is on both lines. If we then equate the corresponding coordinate parametric equations, we should get a solution. But in this case, we get a contradiction in one of the equations, thus we are dealing with skew lines! I also graph out the lines using the GeoGebra 3D graphing calculator and indeed they do not intersect.

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

- Example 3: Skew Lines: 0:00
- Solution to Example 3: 0:45
- Graphing Lines with GeoGebra: 10:10

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