title: Normal Vector of Three Points
body: <p>Hey math geeks, I've got a problem that's been stumping me for a while now. It's for a personal project.</p>
  
  <p>I've got three dots: red, green, and blue. They're positioned on a cardboard slip such that the red dot is in the lower left (0,0), the blue dot is in the lower right (1,0), and the green dot is in the upper left. Imagine stepping back and taking a picture of the card from an angle. If you were to find the center of each dot in the picture (let's say the units are pixels), how would you find the normal vector of the card's face in the picture (relative to the camera)?</p>
  
  <p>Now a few things I've picked up about this problem:</p>
  
  <ol>
  <li>The dots (in "real life") are always at a right angle. In the picture, they're only at a right angle if the camera has been rotated around the red dot along an "axis" (axis being the line created by the red and blue or red and green dots).</li>
  <li>There are dots on only one side of the card. Thus, you know you'll never be looking at the back of it.</li>
  <li>The distance of the card to the camera is irrelevant. If I knew the depth of each point, this would be a whole lot easier (just a simple cross product, no?).</li>
  <li>The rotation of the card is irrelevant to what I'm looking for. In the tinkering that I've been doing to try to figure this one out, the rotation can be found with the help of the normal vector in the end. Whether or not the rotation is a part of (or product of) finding the normal vector is unknown to me.</li>
  </ol>
  
  <p>Hope there's someone out there that's either done this or is a math genius. I've got two of my friends here helping me on it and we've--so far--been unsuccessful.</p>