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

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.