title: How can you orthogonalize a set of vectors
body: <p>I have been reading "Mathematics for 3D Game Programming and Computer Graphics" and there is a chapter exercise (Chapter 2. Question 2) that despite rereading the chapter and researching, I can not seem to understand. How can I "Orthogonalize the following set of vectors" </p>
  
  <p>e1 = ( sqrt(2)/2, sqrt(2)/2, 0 )</p>
  
  <p>e2 = ( -1, 1, -1 )</p>
  
  <p>e3 = ( 0, -2, -2 )</p>
  
  <p>Also, what does it mean to "Orthogonalize a set of vectors"?</p>