It doesn't matter; all that is needed is a consistent unbiased decision.

It would only need 2 cameras (placed at right-angles to each other) since each camera records two dimensions: one for up-down & left-right, another for up-down and back-forward, for example.  These each feed their data to a computer and the software determines where the ball is.  The data from each camera is combined to give the 3D coordinates of the ball at any given time.  The system will be carefully calibrated against the layout of the court, and the virtual court will be an exact replica of the real court. 

Hawkeye processes the data in real-time - exactly how it does this is probably proprietry.  According to Wiki, the system uses 4 cameras.  I suspect this allows it to have two cameras on each side of the net, or there is a lot of redundancy.

Wikipedia provides some answers. wiki/Hawk-eye

It only requires 4 high-speed cameras, much like GPS only actually requires 4 satelites. The rest is down to triangulation and motion equations. Since the position of the cameras and the size of the ball are known the software can work out how far the ball is from the camera. By using at least 2 physically seperate cameras it can work out where the ball therefor is in the court. Comparing its point of impact with a database of the court area allows it to determine if the ball was in or out.

The success of hawkeye is partly technology and partly psychology. Hawkeye's line calls are accurate enough never to be obviously wrong to a human observer.  The software is immune to tennis player outbursts and it makes consistent unbiased decisions.  There is simply no mileage in arguing with a machine.

Briton Paul Hawkins created and named Hawk-Eye, a system which combined the expertise he gained for his PhD in artificial intelligence with his passion for sport, particularly cricket.

In cricket, a batsman can be given out "leg before wicket". This ruling is applied when the umpire believes the ball would have gone on to hit the stumps had the batsman's leg not been in the way. In this situation Hawk-Eye can be used to predict the ball's trajectory and is arguably more reliable than an umpire.

Despite being invented with cricket in mind, it was tennis that was receptive to the technology much earlier, perhaps thanks to TV replays showing that umpiring mistakes contributed to the defeat of Serena Williams by Jennifer Capriati in the 2004 US Open quarter-finals. Hawk-Eye provides an instant replay of crucial shots and has also proved an excellent tool for analysing the strategy and performance of players.

For tennis, it relies upon a maximum of six cameras to provide data for sophisticated triangulation. The position of the ball is tracked via a succession of stills from each camera. Within a virtual recreation of the tennis court, a ray can be drawn from each camera through the centre of the ball. The intersection of these rays provides the position of the ball in three dimensions and, with the passage of each frame, its velocity. This can be used to calculate the contact area of the ball with the court, taking into account the distortion of the ball after it is hit. Hawk-Eye also captures any skidding of the ball on the court, which can deceive the eye into believing a ball is out.

Mike Follows, Willenhall, West Midlands, UK