When you create a new project in Xamarin Studio, you may face below mentioned Error:
This error is caused due to corrupt .zip file of Android.Support.V7 or other nuget packages. This usually occurs when your Internet stops working in the middle of downloading or you force close Xamarin Studio.
The solution to this problem is to delete all the folders from which the error is coming from like "/Users/yourUsername/.local/share/Xamarin.Android.Support.Vector.Drawable" and also all the zips under the folder "/Users/yourUsername/.local/share/zips" and again restart download of Android.Support.V7 or other nuget packages and run your project again
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