# Math in Unity : Vectors (Part I)

Before we move on, we need to understand this :

what is a **Vector**?

If I said that a Vector is a point in a Cartesian plane, would that be right?

For example, if in any 2D project I create a sprite, and put it in this position:

**Vector 2, 3, 0** will be the position of the sprite.

**BUT **there is a difference:

in this case, for example, **2, 3, 0**, represents a POINT shifted by 2 on the **X axis **and 3 on the **Y axis**, starting from

the **ORIGIN POINT**, **0, 0, 0.**

A Vector, on the other hand, can start from anywhere in space, and its measure will be: 2 on X and 3 on Y.

Furthermore, it will no longer represent a point, but a DIRECTION, and its MAGNITUDE will be given by its length.

It is usually represented like this, with an arrow indicating the direction

How do we calculate the length of a Vector?

With the** Pythagorean Theorem.**The formula is this:

**|| v ||**

is the mathematical notation for the length of a vector.

is the mathematical notation for the length of a vector.

In this case our equation is**square root of (2 * 2) + (3 * 3)4 + 9 = 13square root of 13 is 3.60and this is the LENGTH of the vector 2, 3, 0.**

Having a Vector, and knowing its point of origin, we can calculate its destination simply by making the **SUM **of the two Vectors.

**To give a simple example, if our Vector 2, 3, 0 started from the point 0, 0, 0, its destination will be 2, 3, 0.If the starting point were 6, 3, 0, its destination will be 6, 3, 0 + 2, 3, 0the result is 8, 6, 0.**

In both cases, the **DIRECTION **and the **LENGTH **of the Vector are exactly the same.

I wanted to talk about these little basics regarding the Vectors, because in videogames we will have to deal with them many many times.

It is not necessary to have a complex mathematical background to be able to program video games, but since some formulas or concepts will always be present, I think having a basic idea can be very useful.

In the next articles we will look at the Vectors in more detail, with less theory and more practice in code.