In the Buu saga, Vegeta didn't get ssj3 because it was necessary for his arc that Goku was far more powerful than he was. Because that would make Goku less special..
Also, does Vegeta ever get Super Saiyan 3?
Super saiyan 3 is a state, something that's maintained, while a power level is momentary. Goku can sustain ssj3 but Vegeta's power up will only stay there until some minutes after he stops powering up. Ssj3 is hard for anyone and just because Vegeta never ssj3, we think he can't.
Secondly, why can't Vegeta go ultra instinct? A simple answer is because Vegeta thinks too much, so he would not be able to tap into it. When Whis talked about Ultra Instinct, he stated that it would control one's mind and body, and to unlock it, you would have to master the art of moving without thinking.
In this way, when did Vegeta go Super Saiyan 3?
SS3 Vegeta makes his first appearance ever in Dragon Ball: Raging Blast, meeting arch-rival Goku super Saiyan 3 Goku on even terms for the first time.
Does Gohan ever go Super Saiyan 3?
Prior to the SSJ3 transformation, Gohan turns into Great Saiyaman (with a funny animation), then he tranforms into a Super Saiyan, then a Super Saiyan 2 an finally he transforms into a the Super Saiyan 3. When he is in SSJ3 and use the Super energy wave, Gohan is automatically teleported near his opponent.
Related Question Answers
How old is Goku?
Goku was 3 when he came to Earth. 42 years has passed which means Goku is 45 years old. But remember, Goku was dead for 7 years which brings his age to 38.Can Gohan go Super Saiyan God?
The answer is actually no. Gohan's Mystic Powerup IS his Super Saiyan transformation which is why elder Kai tells him to powerup as if he were transforming. The answer is yes. His power was fully awaken and so he had no need to transform into super Saiyan.What is Super Saiyan white?
Super Saiyan White (?????????, Sūpā Saiya-jin Howaito) is an advanced form of the Super Saiyan transformation, and is the final natural evolution of the Super Saiyan God state. It replaces Super Saiyan Blue as the 'ultimate transformation of the Saiyan race'.What is USSJ?
actually ussj and assj is the same thing. ussj is the fanmade term for assj, assj is just ascended super saiyan or saiyajin. assj was the first form of an ascended super saiyan, but it wouldn't work in a fight between cell. ssj2 is the more correct form of an ascended super saiyan, or the form done right.Can Super Saiyan 3 be mastered?
Yes. The Super Saiyan 3 transformation is capable of being mastered in the very same way the basic form of Super Saiyan was in the Hyperbolic Time Chamber. Which would have been extremely fruitful for both a version of Son Goku from Dragon Ball GT and Dragon Ball Super.Is Gohan stronger than Goku?
However, Toriyama still wanted to make Gohan the strongest. We see this when Buu absorbs the other Z-fighters but no one gives him nearly as substantial of a power boost as Gohan does. At this point, Gohan was officially stronger than any of the other Z-fighters. Including Goku.Why ssj3 have no eyebrows?
Due to his baldness, Nappa Super Saiyan 3 form lacks head hair entirely, though his facial hair does grow into a golden beard. Like other male Saiyans, Nappa and Raditz lack eyebrows in their Super Saiyan 3 forms.What is the J in SSJ?
The J in SSJ stands for JIn. It means people/race, so Sayi-Jin means people of the Sayi race.Is Super Saiyan 3 the strongest?
Super Saiyan God, at the very least is 20,000 times more powerful than Super Saiyan 3 - That is how much the gap is between the forms. This logic provides you the idea that SSG is a much, much more powerful form than SSJ3.Why didn't they wish the Saiyans back?
The reason is if he wished the planet back the Saiyans are forever dead. Shenrons rule says you can only revive people who died within a year of making your wish, so it would be pointless to wish the planet back with only him living on said planet. because if he wished them back, they'd just get killed by Frieza 'gain.Can trunks go Super Saiyan God?
Heroes like Son Goku and Vegeta can enter a variety of powerful states from Super Saiyan to Super Saiyan God. However, fans were stunned when Trunks entered a brand-new state during a recent episode of Dragon Ball Super. The hybrid Saiyan underwent the transformation during the '“Future” Trunks' arc.Is ssj3 useless?
SSJ3 isn't useless when fights aren't being dragged out with no God form option. It's a x4 multiplier over SSJ2. That being said it's the worst by power:stamina ratio.Who was the first to go Super Saiyan God?
Yamoshi
Who was the first Super Saiyan 4?
Seeing how bad this situation has become, Vegeta uses Bulma's Blutz Wave Generator to grow a tail and become a Golden Great Ape like Goku. When he finally gains control, Vegeta is successful in becoming a Super Saiyan 4. However, even as a team, Goku and Vegeta still stand no chance against Omega Shenron.Is Vegeta stronger than Goku?
Vegeta is not stronger than Goku. This proves that at the very end Vegeta is stronger than Goku as he can use his new form whenever he needs. But if goku somehow achieves Ultra instinct then he is the strongest. The show makers just want these two saiyans to be nearly same level.Can Vegeta go Super Saiyan God?
Vegeta can go Super Saiyan God in the manga. Vegeta learnt this ki control by training with whis 6 month prior to catch-up to goku, after that both Vegeta and Goku under the supervision of Whis learnt to attain the Super Saiyan God transformation at will(Anime doesnt show Vegeta going SSJ God).How many times has Goku died?
For those looking for a quick answer, Goku has died a total of two times. Once when he was fighting with Raditz and once against Cell.Can Vegeta reach ultra instinct?
Yes. There is a big possibility that Vegeta will learn Ultra Instinct since Vegeta always follows whatever transcended form Goku achieved (except Super Saiyan 3 of course). Besides, he also trained under Whis, so he probably have the concept and idea on how to achieve Ultra Instinct..Can Vegeta Master Ultra instinct?
If Vegeta truly does want to reach Ultra Instinct, he needs to challenge himself as much as Goku has done in the Tournament of Power. Goku has fought incredibly strong opponents so far, and Vegeta simply does not have the same caliber of opponents under his belt. 
