My textbook didn't explain normal form of a line that well, so I'm a quite confused about the example they gave to illustrate the concept further. As follows:

First, how do you get from $\vec{n}\vec{x} - \vec{n}\vec{p}$ to $x + y + z - 2$?

Second, it says "using the row reduction algorithm" ... what do I apply the row reduction algorithm on?

Would really appreciate help!