From Vector to Plane
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]
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.
"From Vector to Plane"
Wolfram Demonstrations Project
Published: March 7 2011