I'm just curious about wether orthogonalprojection generalizes to cases such as this:
Say we have a 1-D subspace L (i.e., a line thru the origin) in R^3 , and let q=(x,y,z) be a point in R^3 which is not on the line. Then I don't see how to project q orthogonally onto L; I can see how to project q into a 2-D subspace P : the projection of q into P is the ortho complement, and every vector in P is in the orthogonal complement of the ortho projected line. But, the same is not the case with q and L. Sorry for the rambling; my question is then actually:
If L is a 1-D subspace of R^3, and q=(x,y,z) is a point not on L. Can we define the orthogonal projection of q into L, or do we need to have a plane P (as subspace) , to define an ortho projection of q?