vect

The root vect comes from the Latin verb vehere — "to carry, convey, transport" — whose past participle was vectus. A Roman ox-cart vehere grain to market; a river vehere a boat downstream. The word was about something doing the work of moving something else from one place to another. From this single image of carrying, English inherited a family that runs from the literal (a car) to the mathematical (an arrow) to the biological (a mosquito) to the verbal (an insult hurled at a person).

Start with the most concrete member. Latin vehiculum was simply the thing that does the carrying — a cart, a wagon. English borrowed it as vehicle: first any conveyance, then specifically a car or truck, and finally, by metaphor, a vehicle for change or a vehicle for expression — anything that carries an idea or effect to its destination. The carrying went from physical to figurative without ever losing the core image.

vector is vectus turned into an agent noun: "the one that carries." Mathematicians borrowed it for a quantity that carries a magnitude along a definite direction — an arrow pointing somewhere. Biologists borrowed the very same word for an organism that carries a disease from one host to another: the mosquito is a vector of malaria. Two fields, one Latin idea — something that conveys a thing toward a target.

The prefixes make the rest of the family. con- (together) + vehere gives convection: heat carried along together by a moving fluid — warm water or air rising and circulating, transporting its heat as it goes. in- (against, at) + vehere originally meant to carry yourself at someone aggressively; that physical lunge became verbal, giving inveigh — to attack someone fiercely in words — and its noun cousin invective, the harsh, abusive language carried against a target.

Several cousins hide their veh under spelling changes: convey and convoy both come (through French) from the same con- + via/vehere family of "carrying along the way," and vex descends from vexare, an intensive of vehere — to shake or jolt someone about, hence to annoy. The pattern across the whole family: a prefix tells you which way or against whom the carrying happens, while vect/veh stays the steady idea of conveyance — making it a close synonym of the roots port and fer, which also mean "carry."