Can you find the argument of the perihelion for this orbit?

Question

At a certain moment, an asteroid has this position in heliocentric ecliptic coordinates. (Distances are in astronomical units.)

x= +0.5877971
y= -2.098983
z= -0.008080998

You are able to determine the inclination and longitude of ascending node for the orbit.

i = 0.003996730 radians
L= 6.170532 radians

You know the true anomaly for that point in the orbit.

Q= 3.14159265 radians

What is the argument of the perihelion for the orbit?

There is enough information in the question to determine the argument of the perihelion. You don't need to know the eccentricity (shape) or the semimajor axis (size) in order to determine the orientation of the plane in space.

Answer 1

Oh that's easy.

1.956097 radians

Answer 2

No, there is not enough information. You would need at least the semi-major axis, and I believe at least one other piece of information like the eccentricity or perihelion distance or something.
Heck, with only the information given in the question the orbit could even be circular. If the orbit is circular, it has no perihelion and so no argument of perihelion.