The two words are entirely unrelated. “Vivacious” comes from the Latin word for “lively” (so it applies only to living creatures such as people and animals), while “vibrant” refers to vibration (i.e. pulsation). You could refer to someone’s personality as vibrant, for example. The meanings of the two words (and each one has a wide range of meanings) are also rather different — you can find the most complete information on each word in the dictionary or your choice (or Google Translate, etc.).

The meaning is very similar but vivacious is used to describe people while vibrant is used to describe places or situations.