Can Digital SLR's zoom in and out whilst recording video?

I googled and found this question: which says it is dependant on the lens type but basically that if you have a zoom lens you can zoom in on a DSLR whilst recording video.

I'm considering purchasing the Nikon D5100 and the Nikon Nikkor 18-105mm lens. Now I know the D5100 has this cool constant autofocus feature whilst recording video, so can I zoom in and out whilst recording video with this camera/lens combo?

Also, are there any youtube videos to help me get to grips with filming on the D5100?

The Sony SLTs do better video than any DSLR.

Yes you can because you can't really lock a zoom lens

If you want a DSLR-type camera that shoots video then you have to include Sony. By using a semi-transparent mirror, Sony SLT cameras are able to use both Phase detection (fast) focusing, and Contrast (detail, slow) focusing, permanently while shooting video. It means that they will outperform any DSLR from Nikon or Canon on the market at this time.

It is worth adding though, that when shooting video of fast moving complex scenes there's no way to really relay to the camera what exact item you want the focus to be on. Not until we get some kind of neural interface…