The cartesian equation of a plane is 2x-y+2z=2. the points in the vector are A(1,0,0), B(0,2,1), and C(-2,0,3). find the vector equation of th eline, perpendicular to the plane, and passing through point (1,1,1) . Find the point E, point of intersection of that line and the plane.

and, the worst of all, find the vector equation of the line, lying int he plane ABC, which is perpendicular to the line AB.

thanks for any help