if an organization is using Agile aproach for project management how is dealing with the Vendors that are not in Agile model and with external entities that are also not in agile approach?

Interestingly, the Agile Practice Guide talks about hybrid approaches for just such cases. I highly recommend it's reading.

The answer is simple: Agile is not about to use a method or life cycle then you can use Agile approach with all methods and life cycle, for example waterfall (it is a life cycle). So, if you have to integrate components is the same that for anything you created: each component has an interface and you have to interact with the component thru the interface. You have to add each component to your main process. In this case, the components are the vendors.

Dora -

A lot depends on the nature of the work that the vendors will be doing. If they are all working independently and there's only occasional integration and verification/validation, then their individual way of working is not an issue. This is essentially a variant of "Water-Scrum-Fall". Certain rules of engagement about the touchpoints have to be worked out, but beyond that, you can support different approaches.

On the other hand, if those vendors are closely interacting on a daily basis amongst themselves and the internal team, then it is important to come up with a common delivery approach and shared working agreements.

Kiron

It has to do with a lot of factors.