How to create an equation for a line in three dimensions given three points : <p>From the equation of a three dimensional line:</p>

<pre><code> f(x,y,z) = A*x + B*y + C*z + D = 0
</code></pre>

<p>The normal is </p>

<pre><code> grad f = [A,B,C]
</code></pre>

<p>The Normal thru Point (x0,y0,z0) is
     [A  .[x-x0
      B    y-y0
      C]   z-z0] = A*(x-x0) + B*(y-y0) + C*(z-z0)= 0</p>

<p>My question is with given three points (x0,y0,z0),(x1,y1,z1), and (x2,y2,z2)
How do you setup the matrix:</p>

<pre><code>[a0 b0 c0 d0
 a1 b1 c1 d1
 a2 b2 c2 d2]
</code></pre>

<p>To solve for A,B,C,D?</p>
