Distance from a Point to a Plane using the Dot Product

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1 year ago
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Health & Science Education math vector algebra 3D science STEM education cross product parallelogram distance

In this video I go over a quick recap on the formula for determining the shortest distance between a point and a plane in 3D. The formula is just the projection of any position vector from the plane to the point onto the normal vector of the plane, and involves their dot product. Contrast this with my earlier method of determining the distance between a point and a line using the cross product and a parallelogram. Note also the similarities between this distance formula in 3D and that of the 2D formula. The full proof for the distance formula between a point and a plane can be found in my earlier video: https://youtu.be/ZxSAc32uIqU

Timestamps:

- Solution to Question 17 (b): Distance from a point to a plane: 0:00
- Distance from a point to a plane formula: 0:07
- Similarities between 3D vs 2D formula: 1:03
- Comparison with distance between a point and a line in 3D: 1:11

Full video and playlists:

- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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