Vector equation of line with angle to a plane

Problem is: Find the vector equation of the line r that contains the point P (1, 1, 1), is parallel to the plane x + 2y - z = 0 and presents a pi/3 radians angle with the plane x - y + 2z - 1 = 0

I let the direction vector of r be (a, b, c) and consider that (a, b, c).(1, 2, -1) = 0, since it's parallel to the first plane. Also, sqrt(3)/2 = (a, b, c).(1, -1, 2) / |a, b, c| times sqrt(6). But then, I'm stuck at a three-variable system with two equations and also a modulus.

How am I supposed to do that? Thanks in advance.