Unit vector? What is it?

Question

This is from Wikipedia:

"In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). "

"The normalized vector or versor of a non-zero vector is the unit vector codirectional with , i.e.,

http://upload.wikimedia.org/math/1/e/5/1e59c738855ef85d7a80ec8c131e276d.png << this is a link to the formula "

so

1- what does normed mean?

2- what does spatial mean?

3- whats a "normalized vector"?

4-what does "codirectional" mean?

5- whats a Unit vector!

u can neglect all the questions, just whats a unit vector? why is it there... like whats the use of it?

"

Answer 1

a unit vector has length equal to one unit.

let us assume a segment &#039;AB&#039; of length &#039;M&#039;

so that  AB = M.

now if we select a length &#039;AT&#039; out of this segment &#039;AB&#039; so that segment &#039;AB&#039;   &#039;g&#039; times length &#039;AT&#039;.

we can write

l(AT) X g = M

Where  g  is a unit vector.

Answer 2

1- what does normed mean?

I think it just means a vector space where a &#039;norm&#039; is defined, that is, there&#039;s a way to find something analogous to the &quot;length&quot; of a vector.

2- what does spatial mean?

Here I think it means the type of vector that comes to mind when you think of an arrow pointing in some direction is space.

3- whats a &quot;normalized vector&quot;?

I believe they are referring to a vector divided by its own magnitude, so that it is scaled down to length = 1.

4-what does &quot;codirectional&quot; mean?

In the same direction.

5- whats a Unit vector!

You can simply call it a vector of length = 1, but that&#039;s sort of misleading.  The real idea is to factor a vector into a product of its length or magnitude times its direction -- the unit vector is purely the direction of the vector. The magnitude of a unit vector is 1 but it isn&#039;t really a length -- it&#039;s a pure dimensionless 1.