What you should be looking at is how to build a shadow-catcher material.
You can look for detailed tutorials online by keywords: “V-ray matte shadow catcher material”.
Basic steps:
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Create a generic material and use a light gray color for it.
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Create a new wrapper material and use the background material as a base
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Set Alpha Contribution to -1
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Turn on “Matte” option
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Turn on “Shadows” option
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Apply the material to faces.
