After going to the bathroom, does one wash with a kli (vessel)? If so, is it three time on right and then three times on the left, or is it alternating right-left three times?

Shalom, One does not need to use a vessel from which to wash with after using the bathroom - except for the first washing of the day on which we say the blessing "Al Netilat Yadayim". There are certainly those who do wash from a vessel, (especially after defecating, as opposed to urinating), and there are sources that say that this is the correct thing to do (see Hilchot Shlomo, 20 footnote 40 - in the name of Rav S.Z. Auerbach zt"l). Some sources write that one should wash three times on each hand, alternatively right, left etc. (see Sharay Tshuva 4, 12, and Piskay Tshuvot 4, 18). However, from the letter of the law it is enough to wash one's hands under the water flowing out of the tap - and I can testify that I have seen great Roshay Yeshiva washing their hands straight from the tap after using the bathroom. My recommendation is that those who have been washing from a vessel until now, or those whose families do so, should continue, where possible to use a vessel. But for those who have no set custom, or in places where finding a cup is difficult (such as in public toilets etc), one can wash directly under the tap. [p.s. - my mother told me that using soap is a good idea!] Blessings, D. Sperling.