The two planes are

x - y + z = 4 and 3x + y - z = 5

I know that a vector cannot be parallel to the planes themselves but to the intersections of the two planes. Uhh, supposedly Im supposed to use a matrix involving

|1, -1, 1|

|3, 1, -1|

|i, j, k |

I'm not sure why we do this step though. Can someone explain how to solve this and why a matrix needs to be used.