Obtaining Normals of a 3D vector

Before I address any 3D stuff in this blog I am going to review the process of obtaining normalized 3D vectors. It is not difficult, but with my penchant to forget everything in five minutes, I consign it to posterity in this post. Below are 3 distances (X, Y, Z) of a 3D vector. The object is to normalize each of them as if the total length (of a 3D hypotenuse) were one;

  (X, Y, Z)

  (5.4, 3.7, 6.2)

Obtain the true total length...

  sqrt(5.4² + 3.7² + 6.2²) = 9.0161

Now simply divide each component by the total length...

  5.4 / 9.0161 = 0.5989  (for X)

  3.7 / 9.0161 = 0.4104  (for Y)

  6.2 / 9.0161 = 0.6877  (for Z)

So our vector, normalized to one, now looks like;

  (0.5989, 0.4104, 0.6877)

And that is it, basically.