Distance Between Two Skew Lines

In this video I go over determining the distance between skew lines, which are lines that are not parallel and don't intersect. To determine this, we can first interpret the skew lines as being on two parallel planes. This just means that we need to determine a single normal vector that is perpendicular to both skew lines. Then, we can simply determine a point on the skew line / parallel plane and use our point-to-plane distance formula. I double check this, as per usual, with the amazing GeoGebra 3D graphing calculator. Note that GeoGebra uses a distance formula that requires knowing both equations of the parallel planes, which I determine the second equation at the end of the video. Here is the link to the GeoGebra calculator so you can play around with it: https://www.geogebra.org/calculator/kccatfbp

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

- Example 10: Distance Between Skew Lines: 0:00
- Applying the Distance Formula Between a Point and a Plane: 8:08
- Graphing with GeoGebra 3D Graphing Calculator: 12:32
- GeoGebra Distance Formula Requires Equations of Both Planes: 14:47

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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