- #1
forty
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Find the matrices of the transformations T which orthogonally project a point (x,y,z) on to the following subspaces of R^3.
(a) The z-axis
(b) the straight line x=y=2z
(c) the plane x+y+z=0
(a) is easy just the matrix [0 0 0;0 0 0;0 0 1]
as for (b) and (c) i have no idea how to work them out. I think (b) might have something to do with projection of a vector on to another... ((u.v)/(|u|^2))u
So maybe v = (x,y,z) and u = a(1,1,2) (a is any real number)
But I'm really stuck on what to do
Any help like usual greatly appreciated :)
(a) The z-axis
(b) the straight line x=y=2z
(c) the plane x+y+z=0
(a) is easy just the matrix [0 0 0;0 0 0;0 0 1]
as for (b) and (c) i have no idea how to work them out. I think (b) might have something to do with projection of a vector on to another... ((u.v)/(|u|^2))u
So maybe v = (x,y,z) and u = a(1,1,2) (a is any real number)
But I'm really stuck on what to do
Any help like usual greatly appreciated :)