How can I view the vendors and their associated purposes on my notice?

Option 1) There's an easy way to see it directly in the vendors' view. For example, for Smart ad server, you need to click on the "view partners" link in your CMP, and then click on the vendor for which you wish to see the purposes.

Option 2) 

1. A) Not IAB vendors : Vendors and associated purposes can be called on /metadata/partners (not the "vendors" but 'partners' section in the following documentation about metadata: https://api.didomi.io/docs/#/partners-storages.)
   Please note that the endpoint partners is not listed in the above but it's the right one to call. 
   
   
2. B) IAB Vendors : the information is nested within the GVL ; https://vendor-list.consensu.org/v3/vendor-list.json