What is the need for normalizing a vector?

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 y

Answer 1

I see the post is very very old, but I still want to answer it because I didn't see clear answer why do we normalize. The reason for normalization of vector is to find the exact magnitude of the vector and it's projection over another vector.

Example= projection of vector a over b is b.cos(theta)

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but in case of dot product the dot product of two vectors a and b is a.b.cos(theta)

which means dot product is projection of a over b times a. So we divide it by a to normalize to find the exact length of the projection which is (b.cos(theta)). Hope it's clear.