In salah it is required to complete a full surah after Al fatihah. Or can we do 3 ayat of a certain surah? And what is the reason behind the ruling if possible?

In the first and second rakʿahs of the daily obligatory prayers, one must recite Sūrat al-Ḥamd followed by another surah; and based on obligatory precaution, [the second surah] must be a complete surah. Also based on obligatory precaution, ‘Sūrat al-Ḍuḥā’ and ‘Sūrat al-Sharḥ’, and similarly ‘Sūrat al-Fīl’ and ‘Sūrah Quraysh’, are counted as one surah in prayers.

If the time for prayers is short or one is compelled to not recite the other surah – for example, he fears that if he recites the other surah, a thief, predatory animal, or something else will harm him – or if one has some urgent matter to attend to, in these cases, he can leave out reciting the other surah. In fact, when time is short and in some cases where one is fearful, he must not recite the other surah.

In recommended prayers, it is not necessary to recite the other surah even if that prayer has become obligatory on account of a vow. However, in some recommended prayers, such as the prayer of loneliness (ṣalāt al-waḥshah), that require a specific surah to be recited, if one wants to act according to the rules of that prayer, he must recite the specified surah.