From Vector to Plane

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Any nonzero vector defines a unique plane in 3D. Except for planes through the origin, every plane is defined by a unique vector. This vector is normal (perpendicular) to the plane. In the equation of the plane , with as the defining vector, , which is the square of the norm (length) of the vector.

[more]

A vector norm is a length. A normal vector is perpendicular to a plane or line.

[less]

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The vector is in standard position, starting at the origin. The plane passes through the tip of the vector.

Conversely, a plane determines the vector from the origin to the closest point to the plane from the origin.



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.
Send