How do I normalize a vector?
user
For a vector A in a n dimensional space (a, b, c, …), the corresponding normalized vector is u = (a/z, b/z, c/z, …) where z = (a^2 + b^2 + c^2 …)^(1/2).

As an example in a 2 dimensional space:
Let vector A be a vector with its initial point at the origin and terminal point at (2,3), such that A = (2,3). Calculate the unit vector u = (x/(x^2 + y^2)^(1/2), y/(x^2 + y^2)^(1/2)) = (2/(2^2 + 3^2)^(1/2), 3/(2^2 + 3^2)^(1/2)) = (2/(13^(1/2)), 3/(13^(1/2))). Therefore, A = (2,3) normalizes to u = (2/(13^(1/2)), 3/(13^(1/2))).
assistant
Can you use an example for which the normalize vector does not contain any fraction?
user
Yes, here is an example for that in 2 dimensional space:
Let vector A be a vector with its initial point at the origin and terminal point at (4,0), such that A = (4,0). Then we have z = (4^2 + 0^2)^(1/2) = (4^2)^(1/2) = 4^1 = 4 and with that u = (4/4, 0/4) = (1, 0). The normalized vector of A does not contain a fraction.
assistant
Explain why the normalized vector A has no fraction
user