title: random unit vector in multi-dimensional space
body: <p>I'm working on a data mining algorithm where i want to pick a random direction from a particular point in the feature space.  </p>
  
  <p>If I pick a random number for each of the n dimensions from [-1,1] and then normalize the vector to a length of 1 will I get an even distribution across all possible directions?  </p>
  
  <p>I'm speaking only theoretically here since computer generated random numbers are not actually random.</p>