What is an example of a situation where vector-based graphics are needed and what are its benefits?
As vector graphics are pixel free and not subjected to scale restrictions, one situation where its use would be best suited is in signage. Signage for businesses encompassing advertising, logo showcasing and even banners (for websites, sometimes) would all be great for utilizing vector graphics as opposed to raster graphics (usually). The benefits of vector graphics include but are not limited to: the file size being smaller than raster images which therefore makes them being stored and shared easier, the easiness to convert to raster format when and if needed and its independent resolution (where altering the size does not hinder the quality of the image).
The only major limitation to vector graphics is its handling of photographic imagery where raster graphics must be used instead. The following example shows a comparison between vector and raster graphics for a sample logo:
Observed is the blurriness and pixelation on the logo on the left as opposed to mathematically generated smooth lines shown with the vector graphic on the right. Other than image manipulation and deliberately creating effects, there is no reason to use raster graphics for anything other than photos or possibly font texture. Ultimately, due to the differences in use, vector graphics and raster graphics need to be done by Illustrator and PhotoShop respectively to attain appropriate results.