# Perpendicular vectors out of a set

I stumbled on this problem and I wanna know if there is a better solution. There are $$n$$ 3d vectors with $$x$$, $$y$$, and $$z$$ components and I wanna find all pairs of perpendicular vectors in this set. Is there any better way than to verify all possible pairs of 3 vectors, some kind of optimization (not the obvious ones)?

• You want to know the better solution, what is your solution? What are obvious optimizations? – Evil Sep 10 at 14:29
• I think this is his solution "to verify all possible pairs" @Evil – narek Bojikian Sep 10 at 17:18

The problem can be solved in time $$\tilde{O}(n^{4/3})$$, using several algorithms: