The Shulhan Aruch (Orah Haim 268) rules that after the recitation of the Amida prayer on Friday night, we recite the verses of "Va’yechulu Ha’shamayim Ve’ha’aretz." Although we recite "Va’yechulu" in the Amida, we recite it a second time after the Amida. The reason for this practice, the Shulhan Aruch explains, relates to the fact that when Shabbat coincides with Yom Tob, "Va’yechulu" is not recited in the Amida. In order to ensure that we remember to recite "Va’yechulu" after the Amida in this case, we recite it after the Amida every Friday night.
The Ritba (Rav Yom Tob of Seville, Spain, 1250-1330), in Masechet Shabbat (119; listen to audio recording for precise citation), writes that it is customary to stand for the recitation of "Va’yechulu" because this recitation serves the function of testimony, as we testify to the fact that Hashem created the world. Since witnesses must stand when delivering testimony, we, too, must stand when proclaiming "Va’yechulu" and testifying about the world’s creation. By the same token, the Ritba adds, one who prays alone does not have to recite "Va’yechulu" after the Amida. Testimony is always given together with at least one other person, and thus one cannot testify about creation alone. Accordingly, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes (268:19) that if one cannot recite "Va’yechulu" together with the congregation, he should have in mind to recite it for the purpose of reading Pesukim, and not for the purpose of testimony. He adds (in Be’ur Halacha) that one should accelerate the pace of his Amida prayer if necessary in order to be able to recite "Va’yechulu" together with the congregation.
The Hazon Ish (Rav Avraham Yeshaya Karelitz, 1878-1953) disputes this ruling (listen to audio recording for precise citation). He writes that the real reason for reciting "Va’yechulu" is the reason mentioned by the Shuhan Aruch (noted above), and not for the purpose of giving testimony. Additionally, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) noted the significance of reciting "Va’yechulu" three times on Friday night – in the Amida, after the Amida, and during Kiddush. Therefore, even if one prays alone, he should recite "Va’yechulu" after the Amida just as he would when praying with the congregation. The Hazon Ish also takes issue with the Be’ur Halacha’s ruling that one should hurry his Amida prayer in order to recite "Va’yechulu" with the congregation. He counters that there is no reason to rush the Amida for the sake of reciting "Va’yechulu" with the congregation, as one can just as well recite it privately. This is also the view taken by Hacham Ovadia Yosef, in Hazon Ovadia – Shabbat (p. 343), where he writes that even a person praying alone recites "Va’yechulu." Hacham Ovadia adds that if a person is reciting "Elokai Nesor" when the congregation reaches "Va’yechulu," he should not join in their recitation, and should instead recite "Va’yechulu" privately afterward. Although one answers to Kaddish, for example, during "Elokai Nesor," this is not the case with regard to "Va’yechulu."
Rav Eliezer Waldenberg (Jerusalem, 1915-2006), in his Sitz Eliezer, writes that if a person recites "Va’yechulu" in the Friday night Amida just as the congregation recites it after the Amida, he may recite it in a loud voice together with the congregation. Just as one recites Nakdishach out loud together with the congregation if he reaches that spot in the Amida at the same time as the Hazzan, similarly, one may recite "Va’yechulu" out loud together with the congregation if he happens to be reciting it at the same time as them.
Summary: Although we recite "Va’yechulu" during the Friday night Amida, we recite it again after the Amida. This applies regardless of whether one prays with a congregation or prays alone. If one hears the congregation reciting "Va’yechulu" just as he recites "Va’yechulu" in the Amida, he may recite it out loud together with the congregation.
