The projection of on is, by definition, a vector in the same direction as and the projection of on is a vector in the same direction as , so of course, the angle between them is the same.
Q: Assume such that , prove that the angle between and is equal to the angle between and
I've tried various things but I have yet to discover a good (formal) way of tackling this. I've written on the first line:
Now I've tried expanding this but I don't think it leads me anywhere so next I write the definition of projection vector:
Here it occurs to me that can be either positive or negative, therefore the projections will be either in the same direction or the opposite direction of and . So this leads me to believe that the projections do have the same angle by the congruence law of intersecting lines(?) Is this somewhat correct? Does it hold for , n>2? How do I format this into a formal proof?