To explain the active and passive adaptors there is some basic fundamental knowledge required of graphics cards and video signals...
Video signals such as VGA, DVI and HDMI all work by using a carrier signal generated by a clock to transmit the Red, Green, Blue, Horizontal and Vertical sync information down the cable.
Displayport however does not use a clock carrier signal as all data sent via displayport is in packets, very much like a network connection with packets of data.
The vast majority of graphics cards provide 2 clock generators / carrier signals, which allow us to connect 2 displays without issue.
In order to use a 3rd display we must use either a Displaport compatible device or if we have only VGA/DVI/HDMI displays available, then we must use an active adaptor, the active adaptors essentially contains a clock gen/carrier signal chip, which is required to be able to connect to VGA/DVI/HDMI.
A passive adaptor does not contain this clock gen carrier signal chip as passive adaptors are to be used when passing the carrier signal from the graphics card, an example of use for a passive adaptor is with the likes of the AMD 5870 E6 card, which sports 6x mini-DP outputs, the first 2 ports may use passive adaptors with the clock gen carrier signal provided by the graphics card, the additional 4 outputs must then use active adaptors.
Or, like the 7970 using DVI + passive DP>DVI + active DP>DVI for your 3 outputs, of cause DVI + HDMI + DP works too.
As for single vs dual...
DVI Single Link = Max resolution of 1920x1200@60hz
DVI Dual Link = Max resolution of 1920x1200@120hz or 2560x1600@60hz
By the sounds of your setup you will need an active adaptor as you
linked to.
I hope you found this information helpful.