Editing Vector projection (section)

===Vector projection on a plane===
In some cases, the inner product coincides with the dot product. Whenever they don't coincide, the inner product is used instead of the dot product in the formal definitions of projection and rejection. For a three-dimensional [[inner product space]], the notions of projection of a vector onto another and rejection of a vector from another can be generalized to the notions of projection of a vector onto a [[plane (geometry)|plane]], and rejection of a vector from a plane.<ref> M.J. Baker, 2012. [http://www.euclideanspace.com/maths/geometry/elements/plane/lineOnPlane/index.htm Projection of a vector onto a plane.] Published on www.euclideanspace.com.</ref> The projection of a vector on a plane is its [[orthogonal projection]] on that plane. The rejection of a vector from a plane is its orthogonal projection on a straight line which is orthogonal to that plane. Both are vectors. The first is parallel to the plane, the second is orthogonal.

For a given vector and plane, the sum of projection and rejection is equal to the original vector. Similarly, for inner product spaces with more than three dimensions, the notions of projection onto a vector and rejection from a vector can be generalized to the notions of projection onto a [[hyperplane]], and rejection from a [[hyperplane]]. In [[geometric algebra]], they can be further generalized to the notions of [[geometric algebra#Projection and rejection|projection and rejection]] of a general multivector onto/from any invertible ''k''-blade.