title: How do I find the plane at which two hyperplanes intersect?
body: <p>In the case of finding the line at which two planes intersect, you need to take the cross product of the normal of the two planes. This cross product is simply taking the determinant of matrix:</p>
  
  <pre><code>i  j  k
  x1 y1 z1
  x2 y2 z2
  </code></pre>
  
  <p>Where (x, y, z) is the normal vector of each plane. The result is a vector parallel to the intersection line. From there you need to find a point which lies on both planes. The two parts combined give you a fully defined line.</p>
  
  <p>How can this be extended to hyperplanes intersecting at a plane? I would assume I would need to take the determinant of a similar matrix, but the matrix I think of:</p>
  
  <pre><code>h  i  j  k
  w1 x1 y1 z1
  w2 x2 y2 z2
  </code></pre>
  
  <p>Is not a square matrix. Also, I don't know how to find a point which lies on both hyperplanes.</p>
  
  <p>Can anyone explain to me how to find the intersection plane of the hyperplanes?</p>
  
  <p>Thanks for your time!</p>