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can i use sqllite3 to manage a big project like shoping site?
Yes.
Should you? Would I? No.
The problem is that you probably have no idea how many users you will have when you start (none would be a good guess) and really no idea how many users in a years time.
And SqLite isn't scale-able, so the first time you find out it doesn't work well enough is when you are popular and can't afford to have the site fail, let alone find the time for a solid rewrite to use a more scale-able system.
Me? I'd probably start with SQL Server, or Azure rather than what is effectively a single user DB being used for multiuser access. At the very least, you get performance monitoring tools which might warn you that you need to consider scale before the site gets problems.