Completing satellite's state vector by given info

[CptHeadCrab]

Homework Statement

A satellite is orbiting Earth with a period time of T=110 min.
At the ascending node, the state vector of the satellite is r_AN =[4500 7100 ?]^T km
At the northernmost latitude, the state vector of the satellite is r_n=[1700 ? 7000]^T km. The question marks imply that the information is missing.

The question asks to complete the vectors, and find orbit's elements: a, e, i, ω, Ω

Homework Equations

Given a state vector of a satellite, r_AN =[x y z]^T km
the latitude is:

there is also the following Kepler rule:

and the 2 body problem generalized solution:

where:

though i don't think the last two would help solving the missing vector.

The Attempt at a Solution

Well completing the r_AN is quite easy as it's known that the ascending node is at the equator plane, thus: r_AN =[4500 7100 0]^T km.

It is also known that the latitude of the northernmost point is the inclination angle (i).

Finding a (the semi major axis) is possible by knowing period time:

was trying to use cross product of r_AN and r_n and thought that the angle between them is the latitude, but then i figured out i was completely wrong.

I think there's some vector calculus to be done but not sure what exactly.
Your help is appreciated.

 

[CptHeadCrab]

Perhaps the angle between the two vectors must be 90 degrees? It might not be the perigee point. Just figured it out by playing with the perigee angle..the northernmost point will remain 90 degrees from the ascending node. What do you guys think?