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homogenizing 4D vectors

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I have a vector v1 = (x, y, z, w) that I want to homogenize and store in v2. I''m not sure if i should... do this: v2 = (x/w, y/w, z/w, 1/w) or this: v2 = (x/w, y/w, z/w, w/w) I''ve always thought that the first method was correct but i''ve seen it done both ways and for my specific application the second method has some advantages over the first (it is symmetric after all). So what''s the proper way.

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The second way is the correct one. The Euclidian space, is the plane in 4D homogenous coordinates, with w=1.

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