I am working on a simple physics based game where 2 balls bounce off each other. I am following a tutorial, 2-Dimensional Elastic Collisions Without Trigonometry, for the collision reactions. I am using Vector2 from the LIBGDX library to handle vectors. I am a bit confused on how to implement step 6 in Java from the tutorial.

Below is my current code, please note that the code strictly follows the tutorial and there are redundant pieces of code which I plan to refactor later.

Note: refrences to this refer to ball 1, and ball refers to ball 2.

    /*
     * Step 1
     * 
     * Find the Normal, Unit Normal and Unit Tangential vectors
     */
    Vector2 n = new Vector2(this.position[0] - ball.position[0], this.position[1] - ball.position[1]);
    Vector2 un = n.normalize();
    Vector2 ut = new Vector2(-un.y, un.x);

    /*
     * Step 2
     * 
     * Create the initial (before collision) velocity vectors
     */
    Vector2 v1 = this.velocity;
    Vector2 v2 = ball.velocity;

    /*
     * Step 3
     * 
     * Resolve the velocity vectors into normal and tangential components
     */
    float v1n = un.dot(v1);
    float v1t = ut.dot(v1);
    float v2n = un.dot(v2);
    float v2t = ut.dot(v2);

    /*
     * Step 4
     * 
     * Find the new tangential Velocities after collision
     */
    float v1tPrime = v1t;
    float v2tPrime = v2t;

    /*
     * Step 5
     * 
     * Find the new normal velocities
     */
    float v1nPrime = v1n * (this.mass - ball.mass) + (2 * ball.mass * v2n) / (this.mass + ball.mass);
    float v2nPrime = v2n * (ball.mass - this.mass) + (2 * this.mass * v1n) / (this.mass + ball.mass);

    /*
     * Step 6
     * 
     * Convert the scalar normal and tangential velocities into vectors???
     */