Yeah running two programs of this sort will not only make each run very slow, it'll slow down your whole computer.
On an other point, it may be me personally but I hated Norton when I had it, it behaved like spyware some times. And if you un-instal it, it's still there on the hard drive like a dead body no one wants hanging around
I now use Avast!, on it's own. It'svery good, is constanly up dated for new viruses, doesnt slow anything down AND it FREE!