We have added our vendor to the project for collaboration and they have accepted the invitation. Now, I can see the name of Vendor in right side bar of the Project page.
But the system is not allowing me invite their team members to this shared project. How to solve this?
All you need to do is ask the Project admin from Vendor organisation to add the team members to the shared project. After that you'll be able to assign tasks to the team members from Vendor's organisation.