I have to minimize $x^Tx$ under condition $a^Tx = 1$. Whats the geometric meanign of this task?
I think that the meaning is to find minimal vector $x$ thats is perpendicular to given vector $a$, but I am not sure.
Whats the difference if we maximize instead of minimization? Thanks for any ideas (I need the teorethical part more than solving this minimization itself - I just dont have imagination for n-dimensional space).