Introduction To Vector⚓︎

Before learning Vector3 you need to know what is a "Vector". Vector is a physical quantity that has a magnitude and a direction. A vector is graphically represented by an arrow drawn parallel to the direction of the vector, The length of the arrow represents the magnitude of the vector.

2D Vector⚓︎

In 2 dimensions, where you have two coordinates/axis X-Axis and Y-Axis. They are perpendicular to each other.

A vector is drawn from the origin (0,0) to the (10,10) coordinate point of the plane. These coordinate points represent the magnitude of the vector on the X and Y axis and are written as (X, Y).

3D Vector⚓︎

In three-dimensional space, There are three axes X-Axis, Y-Axis, and Z-Axis. A 3D vector is the same as 2D but with an extra dimension. The rest of our topic will be based on a three-dimensional vector.

Similar to a 2D vector, coordinates of a vector in 3 dimensions are written as (10,10,10). These coordinate points represent the magnitude of the vector on the X, Y, and Z axis and are written as (X, Y, Z).

Vector in Roblox⚓︎

In Roblox, a Vector3 is a vector in the three-dimensional space. It is created by Vector3.new(x,y,z). Roblox engine uses Vector3 in multiple cases, such as positioning base parts, size of base parts, setting directions of linear velocities, etc. In every case the origin of the vector is different. We will talk about them later. For now, we will go through some common properties of Vector3.

Magnitude of a Vector.⚓︎

For your easiness, Roblox allows you to get the magnitude of a vector by just Vector3.Magnitude. As mentioned earlier, magnitude is the length of the vector. If v is a vector and its coordinates are (10,13,10) then its magnitude is given by

|V| = √(x^2 + y^2 + z^2)
|V| = √(10^2 + 13^2 + 10^2)
|V| =  √(100 + 169 + 100)
|V| = √(369)
|V| = 19.209

Now, in the studio, add the following code in a script and run.

local vector = Vector3.new(10,13,10)
print(vector.Magnitude)

 19.209

It is the length of a vector given in studs.

Unit Vector⚓︎

A unit vector is a vector with a magnitude 1. It can be obtained by dividing a vector by its magnitude. If u is a vector of magnitude (10,13,10) then its unit vector û can be obtained by

û = u / |u|

We will first calculate the magnitude and divide it by every component of the vector.

|u| = √(x^2 + y^2 + z^2)
|u| = √(10^2 + 13^2 + 10^2)
|u| = √(100 + 169 + 100)
|u| = √(369)
|u| = 19.209

Let x2, y2, and z2 be the x,y, and z components of û. Dividing x,y, and z components of u by |u|

x2 = x / |u| = 10 / 19.209 = 0.5205
y2 = y / |u| = 13 / 19.209 = 0.6767
z2 = z / |u| = 10 / 19.209 = 0.5205

We have obtained by x,y, and z components of the unit vector (û). Now the coordinates of û is (0.5205,0.6767,0.5205). If it is a unit vector then its magnitude must be 1. Let's prove that

|û| = √(x^2 + y^2 + z^2)
|û| = √(0.5205^2 + 0.6767^2 + 0.5205^2)
|û| = √(0.2709 + 0.4579 + 0.2709)
|û| = √(1) -- nearly 1
|û| = 1

In the studio, you can easily get the unit vector of a vector by Vector3.Unit.

local vector = Vector3.new(10,13,10)
print(vector.Unit)

0.5205791592597961, 0.6767529249191284, 0.5205791592597961

If you look carefully, you can see it is the same as we calculated. Unit vectors are mainly used for specifying directions. The Direction of a vector and its unit vector always remain the same.

Normal Vector⚓︎

A vector perpendicular to a surface is called a normal vector.

In Roblox, you can find a normal vector in RaycastResult.Normal. This vector is normal to the intersected face. There are many other use cases that you will find when computing vector maths

Closing!⚓︎

I hope it helped in developing a better understanding of vectors and Vector3. Feel free to report this article if there is any mistake. There is a few stuff left regarding vectors and we will discuss them later. For now, bai!

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