How big are plumb tree roots and do i need to plant it a certain distance from the house ?
It depends on the variety and what rootstock it is grafted onto susan3. Do you have any information on the one you are thinking of planting? The majority of them found in GCs and supermarkets etc come on 'St Julian A' rootstock which will eventually result in a tree of about 5m high. I wouldn't risk planting one any nearer to the house than that.
If you don't have that much space you can still grow plums on a dwarf tree (even in a large pot or other container.) In that case look for a 'patio' or 'mini' plum tree which will come on a dwarfing rootstock like 'VVA1'.