You are on the right track so far. A line in a plane (call it M) must be perpendicular to the plane's normal vector. We are told that the line M is also perpendicular to L. Since we know that lines lie along vectors, we can find the cross product of a normal vector of the plane and a vector pointing in the direction of line L, which will be a vector pointing in the direction of line M. You can use this to create your parametric equations and find appropriate values for a, b, and c.