Question

how and when Swami Vivekananda was dead​

Answer 1

At 7:00 p.m. Vivekananda went to his room, asking not to be disturbed; he died at 9:20 p.m. while meditating. According to his disciples, Vivekananda attained mahasamādhi; the rupture of a blood vessel in his brain was reported as a possible cause of death.

Answer 2

He asked all not to disturb him and went to meditation and died at 9:20 pm in 4th July 1902 at age of 39 in Belur Math, Bengal
It means he attained Mahasamadhi