Hey Victor, how are you?
Firstly, you should know that "take a vacation" means "to go somewhere for a vacation; to stop work to have a vacation." I must say that I agree with Chris upon the difference in the usage of the word ''vacation'''. So, your first sentence, which is "He takes a vacation at his grandmother's house" sounds correct to me. As for your second one, it does not sound correct as "take vacations" is not considered to be a standard idiom in English (that is why I disagree with Nick upon his second statement). However, you might use the word "vacation" as a verb and say "He vacations at his grandmother's house" or ''During his vacations, he stays (or ''would stay'', if you were to express a repeated or habitual action in the past) at his grandmother's house.''
Below you shall find a set of useful examples:
E.g.: "Sara took a vacation at the Grand Canyon last year."
E.g.: "I need to take a vacation and relax."
E.g.: ''I have heard he is planning to take a vacation by the end of this month.''
E.g.: ''Where do you usually take a vacation (at)?''
*NOTICE: The form ''have a vacation'' is also permissible in English. You could say, for example ''I had a one-week vacation at my uncle's farm'' or ''I plan to have a vacation next month''.
Hope that helps!
Should you have any further questions/doubts regarding English grammar, do not hesitate to contact me. I shall be pleased to help.
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