I have considered a very interesting question myself, and I think it is very difficult to answer it.

Consider $N$ $n$-dimensional vectors, where the angle between any two vectors is acute and their starting point is at the origin，Can we rotate these vectors together so that the coordinate components of each vector are positive?

Thank you very much.

Consider $N$ $n$-dimensional vectors, where the angle between any two vectors is acute and their starting point is at the origin. Can we rotate these vectors together so that the coordinate components of each vector are positive?

I have considered a very interesting question myself, and I think it is very difficult to prove it， N n-dimensional vectors, where the angle between any two vectors is acute and their starting point is at the origin，Can we rotate this vector group so that the coordinate components of each vector are positive？ I think everyone is very smart. Can you help me solve this problem? Thank you very much

I have considered a very interesting question myself, and I think it is very difficult to answer it.

Consider $N$ $n$-dimensional vectors, where the angle between any two vectors is acute and their starting point is at the origin，Can we rotate these vectors together so that the coordinate components of each vector are positive? 

Thank you very much.