Primary and secondary question

[Mark Ngo]

I have a domain called foobar.com and it is located in UK.  The primary
name server is in UK while the secondary is in US.  The primary server
delegated us.foobar.com to US DNS.   To resolve fo.us.foobar.com from
US, must I have to go to UK fist then go to us.foobar.com name server?
Or it uses the shortest path, which is the secondary US name server.

Thanks in advance.