Question

Trying to understand vectors a bit more.

What is the need for normalizing a vector?

If I have a vector, N = (x, y, z)

What do you actually get when you normalize it – I get the idea you have to divide x/|N| y/|N| & z/|N|. My question is, why do we do this thing, I mean what do we get out of this equation?

What is the meaning or ‘inside’ purpose of doing this.

A bit of a maths question, I apologize, but I am really not clear in this topic.

Answer 1

That’s a bit like asking why we multiply numbers. It comes up all the time.

The Cartesian coordinate system that we use is an orthonormal basis (consists of vectors of length 1 that are orthogonal to each other, basis means that any vector can be represented by a unique combination of these vectors), when you want to rotate your basis (which occurs in video game mechanics when you look around) you use matrices whose rows and columns are orthonormal vectors.

As soon as you start playing around with matrices in linear algebra enough you will want orthonormal vectors. There are too many examples to just name them.

At the end of the day we don’t need normalized vectors (in the same way as we don’t need hamburgers, we could live without them, but who is going to?), but the similar pattern of v / |v| comes up so often that people decided to give it a name and a special notation (a ^ over a vector means it’s a normalized vector) as a shortcut.

Normalized vectors (also known as unit vectors) are, basically, a fact of life.