The projection is symmetric only when u and v have same length. If we have a very short v and a very long u, apparently the projection of v onto u is shorter than the projection of u onto v. When we have two non-unit vectors, we need to divide the inner product by the length of the vector being projected to get the projection. v'=<v,u>/|u|.
The projection is symmetric only when u and v have same length. If we have a very short v and a very long u, apparently the projection of v onto u is shorter than the projection of u onto v. When we have two non-unit vectors, we need to divide the inner product by the length of the vector being projected to get the projection. v'=<v,u>/|u|.