Even though he is evil at heart, Vegeta is perhaps one of the most strong-willed characters in the series. Like Son Goku, he is extremely industrious, constantly striving to be better, but different purposes drove Vegeta's spirit. Goku fought to defend the lives and others and to challenge his limitations while Vegeta fought to satiate his bloodthirsty appetite and die hard pride, which is unwilling to accept defeat. This gradually changes throughout the series.
The primary driver of his will is Son Goku. Vegeta's defeat in his first encounter with Goku and his unwillingness to accept Goku being more powerful had constantly fuelled his strong will to continue to train himself. After seeing Goku turn into Super Saiyajin and defeating Freeza, he grew even more jealous of Goku’s achievements and immersed himself in intensive training. After much sweat and frustration, he finally became Super Saiyajin. He only enjoyed a fleeting moment of pride in destroying #20, before being defeated by #18.
Vegeta’s first catharsis occurred during Son Gohan’s battle with Cell. Because of his rash decision to attack Cell when he did not have the power to, had caused Gohan’s arm to be seriously injured when Gohan saved his life. Not only was he not even close to Cell’s ability, but also served as a hindrance to Gohan. That was the first time Vegeta accepted his incapabilities by making an apology to Gohan.
By the time Majin Buu appeared, what used to be a cold-hearted Vegeta changed. Right before he proceeded to sacrifice his life in an attempt to destroy Buu, he told Trunks that he cared about him and how he felt bad about giving Trunks much less attention then Trunks deserved.
During Son Goku's final battle with Majin Buu, Vegeta goes through a complete catharsis. He realized that Goku's pure and kind heart gave Goku the power that Vegeta never had. He finally realizes that the good ultimately prevails.
Bulma:
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Bulma appeared at the very beginning of dragon ball. She ran into goku at the stasrt of the series. Bulma has since then alinged herself with Goku. In DB she, along with Goku, searched for the dragon balls. Later in DBZ, we find that Bulma's father, Dr. Briefs, is head of a company known as capsule corp. Bulma is his asssintant as they begin to invent many things.
Bulma, like Chi Chi, adds some comic releaf to the series. In the Freeza saga, when she goes along with Kurririn and gohan in search of the namekian dragonballs, we always find her trying to be in charge and bossy. However, when something bad happens, she constantly freaks out. As the series of DBZ progresses, you will find that Bulma goes through many hair changes. She also becomes head of the capsule corp and matures a bit.
Early in the Cell Game, we find out that Bulma had slept with Vegita and had a baby named Trunks. Through the Cell series, she took care of trunks. In the Buu series, Trunks gets older and Bulma begins to give him a little more freedom.
Trunks:
Trunks is the son of Vegeta. He first arrives in the DBZ series in the Freeza saga. He is a young teen at his arrival and wields a very powerful sword. Trunks explains to the Z warriors that he is from the future and originally came back to the past to heal Goku of his heart condition and stop the androids from destroying the Earth. Later in the series, chibi (little) Trunks is finally born. after the androids were destroyed Marai (Future) Trunks returns to the future.
Near the climax of the series, we see Trunks as a young kid. He trains with Goten and his father, Vegita. Trunks has a strong will to fight, and is set to be just as strong as his father. He and Goten become very good friends and are always hanging around each other.
When fighting against Majin Buu, Trunks learned the fusion dance along with Goten to form the powerful Gotenks. Though Trunks is very outgoing, he is also very naive as a kid thus always seems to wind up in trouble. At the end of the DBZ series, Trunks becomes the teen he was earlier as future Trunks.
