Vegeta is the so called "Prince of Saiyans". He is also the father of Trunks and the husband of Bulma(isn't he lucky). He came to Earth on a mission to destroy it. He failed and was defeated by Goku. Since that day, Vegeta's new goal and purpose to live is to be stronger than Goku . When Vegeta goes on Namek to get the dragon ballz before Frieza , he sees Gohan and Krillin. He uses them to help gather the dragon balls. When Frieza finds out the dragon balls are together he seeks out and finds them. To make a long story short , Vegeta was killed by Frieza in front of Goku. Vegeta, before he died , saw how strong Goku was and realized that Goku was a super saiyajin. Vegeta was eventually wished back and he went off training to be a super saiyajin. He accomplished this and saved Goku's life before android 19 killed him. Vegeta after the android saga and during the cell saga sees that Goku , Gohan , and even his own son surpass him in strength. When Goku kills himself by teleportin him and cell to kaio samas (king kai's) planet, Vegeta is mad because Goku died with confidence and ease and because he never got a chance to prove his strength to Goku. He is a true "Saiyan Prince" . He is not arrogant , its his pride as a Saiyan.
