Vegeta becomes super sayian 2 when he doesn't kill Majin buu. When he came back to help goku defeat super buu.
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160 is when he first went super saiyan 2 after training with goku (his dad) as a super saiyan 1 he was angry because cell killed so many people and killed one right in front of him so he got angry and went SUPER SAIYAN 2. P.S super saiyan 2 is the highest super saiyan gohan can do but in dragon ball AF gohan goes super saiyan 4 and goku goes super saiyan 50 that is all i can tell you.
He doesn't hate him, but they're rivals. He gets angry at Goku because Goku is far stronger then him and he is supposed to be the Saiyan prince (the best) . Vegeta hated Goku, because the Earth raised Saiyan is stronger than him. Vegeta failed to win against or kill Goku when he first landed on Earth. He further hated Goku when he became the first Super Saiyan in thousands of years and went on to defeat Frieza. Vegeta believes that since he is the Prince of all Saiyans he should have been the first Super Saiyan and he should have been the one to kill Frieza to avenge his people. Most of all he despised Goku because he the Prince is weaker than a 3rd class Saiyan.
episode 35
Episode 207, "Take Flight Videl", while at 150x gravity and vegeta punches him in the face. Hahahaa
Yes,when Frieza killed Krillin on Dragon Ball Z Kai.