Another Vector Problem?

Question

Find an x - y - z equation for planes 7-10.

The plane through Po = (1,2, -1) perpendicular to N =

i + j

Answer 1

The plane through P(x_0, y_0, z_0) with normal vector <a, b, c> is a*(x - x_0) + b*(y - y_0) + c*(z - z_0).  In this case, the normal vector is <1, 1, 0>, and so the equation of the plane is (x - 1) + (y - 2) = 0, or x + y = 3.