Vector and Scalar Equations of a Plane

In this video I go over planes in 3D and derive the vector equation of a plane and then convert that into scalar equations of a plane. A plane can be described by a point on the plane and a vector perpendicular to the plane. This perpendicular or orthogonal vector is called a normal vector. We can obtain a formula for the plane by noting that the dot product is equal to zero for perpendicular vectors. And then we can take a vector on the plane and towards the point on the plane and compute the dot product with the normal vector to obtain the vector equation of a plane. If we expand this vector equation by writing out its components and expanding out the dot product, we obtain the scalar equation of a plane.

I also go over an example on determining the equation of a plane, and as usual use the amazing GeoGebra 3D graphing calculator to graph out the plane. You can play around with the GeoGebra calculator here: https://www.geogebra.org/calculator/yrgywmbr

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

- Vector Equation of a Plane: 0:00
- Scalar Equation of a Plane: 6:02
- Example 4: 8:02
- Graphing Plane with GeoGebra 3D Graphing Calculator: 13:38

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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