# How do I find a unit vector of another in Java?

I'm writing a Java formula based on this tutorial: 2-D elastic collisions without Trigonometry. I am in the section "Elastic Collisions in 2 Dimensions". Part of step 1 says:

Next, find the unit vector of n, which we will call un. This is done by dividing by the magnitude of n.

My below code represents the normal vector of 2 objects (I'm using a simple array to represent the normal vector).

int[] normal = new int[2];
normal[0] = ball2.x - ball1.x;
normal[1] = ball2.y - ball1.y;


I am unsure what the tutorial means by dividing the magnitude of n to get the un.

What is un? How can I calculate it with my Java array?

First off, using arrays is not the best way to represent Vector information in Java. Second, use floats. Take a look at LibGDX Vector2 class.

The magnitude of a vector is it's length, obtainable with the Pythagorean theorem:

a² = b² + c²


in your case, you can obtain it by:

float[] normal = new float[2];
normal[0] = ball2.x - ball1.x;
normal[1] = ball2.y - ball1.y;
float magnitude = (float)Math.Sqrt(normal[0]*normal[0] + normal[1] * normal[1]);
float[] un = new float[2];
un[0] = normal[0] / magnitude;
un[1] = normal[1] / magnitude;


let me reassure you that using Arrays is NOT good. With a properly Vector class it should be like:

Vector2 normal = new Vector2();
normal.set(ball2);
normal.sub(ball1);
Vector2 un = new Vector2();
un.set(normal);
un.normalize();


If you were going to a language where Operator overloading is possible:

Vector2 normal = ball2 - ball1;
Vector2 un = normal / normal.length();

• Thanks very much for the help! I will try to implement this and let you know if it works out. Currently I am not using LibGDX library so I cannot use Vector2, Thanks! Jun 4, 2014 at 2:58
• I took your advice and started to work with Vector2, while I am not using LIBGDX, I did copy over the Vector2 class and am using that for calculations. Definetly a better approach to arrays. Cheers! Jun 9, 2014 at 14:39