There is a hose that is leading to no where. 2005 hemi 5.7 liter engine. The hose is not attached to anything but is simply capped at the top by the oil dip stick (small grey cap in the middle of the pic by the dip stick). The other end was just hanging and so I saw what appeared to be the connection for it but want to find out what this hose is for. Is this now connected correctly?

 

It's a vent line. The photo shows it attached to a metal line on the front differential cover. The differentials need to have a vent to allow expansion of the air inside when the gears get hot. (They do when you're driving for a while.) The long line is to get it high enough to stay out of any water you might run through on a rainy day. The vent on the end is to let air in and out but keep dirt from falling in.