Linear Algebra - Closest point in a plane

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Given a point b and a plane, find the point in the plane closest to b.

Closest Point Plane

By Linear Algebra - Plane, we can assume the plane includes the origin.

The plane is a vector space V. Let {v1, v2} be a basis for V.

Goal: Given a point b, find the point in Span {v1, v2} closest to b.


  • v1 = [8,-2, 2] and v2 = [4, 2, 4]
  • b = [5,-5, 2]
  • point in plane closest to b: [6,-3, 0].

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