Vegeta was a warrior of superior class among the Saiyajin. Before Vegeta, the strongest Saiyajin was his father, and when Vegeta's power exceeded that of his father while he was still a kid, his arrogance grew, further instilling his belief that he would be the strongest, giving him the right to look down on everyone else, because on Planet Vegeta, power was everything. And then there were Freeza and his henchmen. So even though Vegeta knew that he was the strongest of the Saiyajin, he also knew that there were other races that were more powerful. However, the Saiyajin race was the ultimate warrior race. Vegeta knew that with time, he would eventually surpass Freeza's hecnhmen, and perhaps even become the mysterious Super Saiyajin, the
one who legends foretold as the strongest in the universe, the one who even Freeza would be no match for. Vegeta's dreams were crushed when he suffered defeat at the hands of an inferior warrior, Kakaroto; or as his earthling friends call him, Son Gokou. What was even more devastating was that this Kakaroto.. this.. Son Gokuu, displayed powerthat far surpassed even the royal prince himsel while fighting against Freeza's hired goons on Planet Namek, and in the end Gokou ended up turning into the legenday Super Sayain and defeating Freeza,while Vegeta had lost his life fighting Freeza This was just the begining of Vegeta's probelms. Gokou would surpass him at many other times, but Vegeta was always one step behind. He too turned into the legendary Super Sayain and any time Gokou got stronger he would up himself too. Vegeta was always a very agitated man then only care about himself and being the strongest person alive. Vegeta showed a glimpse of care for his son Trunks when cell
basically came back from the dead and then almost killed trunks. Vegeta lost control charged at Cell with everything he had, even though he knew he couldn't win. It wasn't until The Majin Buu saga after he killed himself in order to save his son Trunks and Gokou's son goten that his compasion truly shined through, and well I don't wanna give away the ending of Dragonball Z but lets just say that you should really be pround of Vegeta.
Vegeta's Family
Father: King Vegeta I
Father-in-law:Dr. Briefs
Mother-in-law:Mrs. Briefs
Wife:Bulma
Son:Trunks
Daughter:Bra