When you do something vehemently, you do it with energy and passion. If you vehemently oppose your brother’s plan for the family vacation, then you’re really, really against it.
The word vehemently has a lot of force behind it. It traces back to the Latin word vehement, meaning “impetuous, violent.” If you do something vehemently, then you do it forcefully and with emotion, and no one will doubt how you really feel. You’ll often hear it used to describe situations involving conflict or disagreement. If you vehemently deny your involvement in the incident with the lawnmower, then you deny it very strongly.