Equation of a plane (General and Point-Normal Form)

maze

You got the normal by cross product: n = (9,1,-5)

Now since the normal is perpendicular to any vector parallel to the plane, and since (x-p1) is parallel to the plane if x is on the plane, we have

0 = n*(x-p1)

0 = (9,1,-5)*((x1,x2,x3)-(1,2,-1)) = (9,1,-5)*(x1-1,x2-2,x3+1)
0 = 9*x1 - 9 + x2 - 2 - 5*x3 - 5
0 = 9*x1 + x2 - 5*x3 - 16

So there you go, thats the equation for the plane. You could divide the whole thing by 16 to get the results the book talks about.

Damascus Road

Thanks again, maze.

If all 3 points are on the plane, what makes you choose (x-p1) ?

maze

You could choose any point on there. Give it a try for p3 and see what happens!