title: Given two points and two direction vectors, find the point where they intersect
body: <p><strong>EDIT: THIS IS NOT A DUPLICATE, please read the description of the problem</strong></p>
  
  <p>Just to be clear, these line segments does not have an end point. They start at a point and goes to infinity based on a direction vector. I've found solutions for finite line segments, but they do not apply in this particular case (I think).</p>
  
  <p>So, the title is basically my entire question - I've got</p>
  
  <ol>
  <li>point p1</li>
  <li>point p2</li>
  <li>direction vector n1 (a normalized vector)</li>
  <li>direction vector n2 (a normalized vector)</li>
  </ol>
  
  <p>The first line segment starts at p1 and points towards n1</p>
  
  <p>The second line segment starts at p2 and points towards n2</p>
  
  <p>I need two answers:</p>
  
  <ol>
  <li>If they intersects and</li>
  <li>What is the point of intersection</li>
  </ol>
  
  <p>I've found these two answers, but I'm so bad at math that I could not adapt them to fit my problem, but it could help you guys, I hope.</p>
  
  <blockquote>
    <p><a href="https://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect">How do you detect where two line segments intersect?</a></p>
  </blockquote>
  
  <p>and</p>
  
  <blockquote>
    <p><a href="https://stackoverflow.com/questions/14256525/given-two-points-and-two-vectors-find-point-of-intersection">Given two points and two vectors, find point of intersection</a></p>
  </blockquote>
  
  <p>Thanks a lot!</p>
  
  <p>Edit: (BTW, I'm working at 2D Space, so you don't have to worry about the z axis, thanks)</p>