Solve each of the following systems of equations. Give a geometrical interpretation of each system and its solution.
1. x - y + 3z = 4
2. x + y + 2z = 2
3. 3x + y + 7z = 9
OK so the first thing I did was check to see if any of the equations were scalar multiples, to see if any of the planes were coincident, which they weren't. Then I checked their normals to see if they were scalar multiples to see if the planes were parallel, they weren't.
Then I took the triple scalar product to see if the normals were coplanar. They were. From this I said the planes either have one line of intersection, or they have no solution, because they have three separate intersections as a triangular prism.
I do not know how to determine which possibility it is, the answer says it has no solution, it forms a triangular prism.