Name: Distance From a Point to a Plane + Proof
Uploaded: 2023-07-31T21:46:37+00:00
Duration: 10 min 50 s
Description: In this video I derive the formula for the distance between a point to a plane in 3D coordinates. The distance formula can be derived by taking the scalar projection of a vector from a point on the pl

2 years ago

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vectors distance from a point to a plane 3d coordinates vector algebra geometry 3d geometry science mathematics math stem distance

In this video I derive the formula for the distance between a point to a plane in 3D coordinates. The distance formula can be derived by taking the scalar projection of a vector from a point on the plane to the desired point and projecting it onto the normal vector perpendicular to the plane. We can then utilize the geometric interpretation of the dot product to get a formula involving cosine and our desired distance. Further algebraic simplification yields the distance formula.

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

- Example 8: Distance from a Point to a Plane: 0:00
- Distance = Absolute Value of Scalar Projection: 1:15
- Distance Formula: 10:20

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