Vegeta and Goku have a very close relationship. I'd say they share a bond even stronger than what Goku share's with someone like Krillin. They might not be friends that hang out together, laugh and have a normal conversation but they see each other as source of motivation to help better themselves and become stronger, that makes them more ambitious.
It might look as though Vegeta hates Goku but in reality, it's just his personality and the way he is which also brings a comedic aspect to the show. Vegeta has a very cocky and arrogant personality and also him being the Saiyan prince is responsible for the same. He considers his race to be superior to all other beings and he's the kind of guy who likes to assert his dominance over all other beings by using his power. Goku on the other hand, trains purely out of love for combat and doesn't share the same motivations as Vegeta which is one big difference between their personalities.
Vegeta always had a mutual respect for Goku but I recommend you watch the fight between Kid Buu and Goku where Vegeta acknowledges Goku's superiority and has a new found respect for him. Even in Dragon Ball Super, it might appear as though Vegeta doesn't like Goku but if Goku's life were at risk, Vegeta would step in and help him. This is seen when he catches Goku after Beerus knocked him out. Also when Freiza was about to kill him, Vegeta steps in. Even during the tournament of power, we see Vegeta step in to help Goku while he was being attacked by Universe 9.
In simple words, Vegeta is jealous of Goku's strength. He has admitted this a couple of times, although his arrogance and massive ego doesn't want him to accept him being weaker than another saiyan which is why we see him display some form of anger when he sees Goku and not cause he hates him.