Vector has a lot of definitions but in the field of biology, it is a technical term for an organism that transmits a pathogen from one animal to another. For example a mosquito might feed on someone who has malaria, become a carrier for malaria, and then transmit the malaria to the next person it feeds on.
A vector can be different things in different fields of study. americalibre covered the biology side of it very well. In math, engineering, and physics, a vector is a tool that you can use to calculate other things. Given the magnitude and direction of a vector, one can figure out where something will go. This is especially useful to environmental engineering when people are trying to figure out what will happen to a pollutant that is released into the atmosphere out of a smokestack.
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