# From Vector to Plane

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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.

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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.

## Permanent Citation

"From Vector to Plane"

http://demonstrations.wolfram.com/FromVectorToPlane/

Wolfram Demonstrations Project

Published: March 7 2011