At the scale we're talking (that is, individual pixels) the vectors would need to have many control points in order to properly render at the small size. Due to that high count of points plus the overhead of the math figuring out what to draw, it ends up being slower than rendering a bitmap. Try it in Flash. Anything under about 100x100 pixels that has high detail should be a bitmap.
Well, no. As has been pointed out, the raster images can be cached. Not only that, they can be pre-rendered. With no zooming at all, there would be zero speed difference, because all you would see would be pre-rendered vector images. What it gives is scalability-- you can actually add zooming for those that can take the hit, and you can support more resolutions with similar proportions, or whatever.
Its actually a good thing that computers went the route of rasterized images, as if we'd gone vector then the digital art community would never have sprung up the way it did. Not to mention that our games wouldn't have the graphics we have now (imagine trying to use vectors to define textures on a 3D polygon!).
The irony being that polygons are vector shapes. 3D graphics today was the success of a combination of 3D vector imagery and 2D raster textures, and the failure of the direct 3D analogue to pixels, voxels-- though voxels have their place, and may be making a comeback (they might be handy with real-time ray tracing, but that technology's not going to pan out for a very long time, if ever).
What were those vector's again? And I have heard vector-based graphics but don't know what it is....
Math vectors are simply collections of scalar values-- numbers. For example, (3, 5) is a mathematical vector, so is (7, 5, 2). Every vector here can be used to define an equation-- for example, 2x + 5, and 7x
2 + 5x + 2 are polynomial vectors that can be represented using simple vectors as explained above. You can in fact draw a line using a polynomial expression as a function.
In vector rendering, you don't quite do this-- a single vector doesn't define a line, but a sequence of vectors does. Each vector contributes to a part of a polynomial expression that determines the shape of a line (the polynomial is actually parametric, meaning that the line can cross over itself, and so on). It's the same idea, though-- each vector contributes to the shape of the line in a similar fashion to how each element of a vector contributes to the shape of a simple polynomial expansion.
This is compared to raster graphics, where you just have a bunch of points with a defined color (can also be defined mathematically using vectors, of course, but hey), and where you just draw each point as a box/pixel with that color. Zooming in can only expand the box, not the thing that box is meant to represent-- a bullet or a hammer or whatever-- whereas a vector line would define the entire outline of the bullet or hammer, and represent it as accurately and efficiently as possible using boxes/pixels at whatever resolution you have set.