Three Points Determine a Plane

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Three noncollinear points in three dimensions determine a unique plane with an equation of the form , where and is the positive distance of the plane from the origin. The vector is normal (perpendicular) to the plane and has norm (length) equal to 1.


For such an equation, the signed distance from a point to the plane is given by . Points on the same side of the plane have the same sign.


Contributed by: Ed Pegg Jr (December 2017)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.