It's dependant on the hardware, the CPU needs to support the 64bit instruction set. There's a lot of VAIO's around so you'd have to check the specs online to see if they support X64 Windows.
That processor has Intel 64, so you could install x64 Windows if you want.
On an unimportant note, it's not x32, it's x86. In the 90's all Intel processors were a number then 86, 386, 486, 586, 686. Then AMD brought out Athlon 64 and it was x86_64 which is contracted to x64.
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