let a be a point on the plane let n be the vector that is perpendicular to the plane and let r be any point on the plane. the vector going from a to r is a direction vector and is perpendicular to the normal as it lies in the plane. therefore (r-a).n = 0 and this can be written as r.n = a.n . that is how you write the equation of a plane in vector form.
You are given a point on the plane, so all you need to do now is find a vector perpendicular to it. the normal will be perpendicular to the direction of the line (1 , 0 , 1) and then vector going form (1 , 0 , -1 ) to ( 1, 1, 1). you need to find a vector perpendicular to both (1 , 0 , 1) and (0 , - 1 , - 2). to find the vector take the cross product of the two vectors.