why nslookup could not find my domain?

[TAT LUK]

	I am running BIND-4.9.7 on an NT 4.0 platform. Both
	the forward and reverse lookup tables are setup
	correctly. From my network, when I do a ping to a host 
	within my network, it works fine. When I do a nslookup with
	the same address, it works fine also.

	When I try it from an external ISP and use
	their DNS, pinging to the same host has no problem, yet
	nslookup for that address failed to resolve the host name.
	If I force the nslookup to use my DNS, then both ping and 
	nslookup will work from the external ISP. Is there
	any reason why nslookup does not work for me from the 
	external ISP (or the Internet)?
	
	I also noticed that there is a form called "in-addr.arpa" 
	registration form from Internic. I understand it is for reverse
	address lookup but can someone help me to better
	understand the purpose of this form and what would
	happen if I have never submitted this form for our domain?

	Thanks.

	Tat Luk