64 bit VM on 32 bit OS with enable vt-x feature

Yes.. try Sun Virtual Box, its a free download and available for most of the platforms.

I use it for all my testing purposes, its even has Direct 3D acceleration for running some basic games on your VM.
 
How is Intel VT related to supporting 64 bit guest on a 32 bit OS?

AFAIK, It is dependent on Virtualization solution you use.
 
Just try this,

Go to your ESX machine BIOS and disable (if not already) intel VT and reboot. Now install 64 bit OS on ESX and notice that it will prompt you to enable VT. So it indeed is required, not exactly know the intenel reason though, searched online and found this on wiki, see if it clarifies some thing.

<wiki>
One of the peculiarities of the x86 architecture is that page-level protection is provided by the hardware only between rings 0 and 3. In order to protect the memory of the hypervisor (ring 0) from a guest OS running at ring 1, segmentation must be used.[13]:22 The initial version of x86-64 (AMD64) did not allow for a software-only full virtualization due to the lack of segmentation support in long mode, which made the protection of the hypervisor's memory impossible, in particular, the protection of the trap handler that runs in the guest kernel address space.[14][15]:11 and 20 Revision D and later 64-bit AMD processors (as a rule of thumb, those manufactured in 90 nm or less) added basic support for segmentation in long mode, making it possible to run 64-bit guests in 64-bit hosts via binary translation. Intel never added segmentation support to its x86-64 implementation (Intel 64), so 64-bit software only-virtualization is not possible on Intel CPUs, but Intel VT-x support makes 64-bit hardware assisted virtualization possible on the Intel platform.[16][17]:4
</wiki>

taken from x86 virtualization - Wikipedia, the free encyclopedia

By the way, I sits on First floor ;).
 
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