When backpacking for extended periods, 10 - 20 miles a day, in rough terrain, weight matters. I've been known to cut the handle of my toothbrush so as to save weight. This is especially true if you're hiking at altitude, and even more true if you simply aren't used to backpacking, and so might not be in the best shape for it.
So if you're really going to backpack, you need to think long and hard about how much that knife weighs.
Since you're carrying everything you need to survive, I suggest you look into a neck knife style of knife. Make it small and light and able to hang on a lanyard around your neck. This will be the easiest thing to access, no matter whether you're wearing your pack or not.
If they were still available, I'd suggest a Becker Necker. Since those are now really hard to come by, maybe a
RAT-3 is a good suggestion. I'm also looking into Bark River Micro Canadians, but I'm not sure if they're strong enough to handle a "lost my pack in the river" scenario, so I don't want to recommend them yet.
Alternatively, you can look into ultra light backpacking techniques, and then carry a bigger knife. You'll need the bigger knife to help prepare your campsite because you won't be carrying as much with you in that scenario.
I would never bother with a hatchet or a big knife or an axe

eek: ) for backpacking. The weight alone is prohibitive. A folding camp saw, at the most, is what you'll need for that campfire. But you shouldn't
need a campfire because you've got your sleeping bag, camp stove, and tent/slitarp with you, right?
4 - 6 inches, max, on a fixed blade when backpacking, and if you're going 6 inches then you need to be looking into ultralight techniques so you can save weight somewhere else.
Before heading out into the wilderness on a backpacking trip, I suggest a weekend with just whatever knife you carry and your PSK (both of which should ALWAYS be on your body). Make a shelter and a fire and hunker down for for a night or two. Make sure you can get by on just those things for ~48 hours. Because there's always a non-zero chance that you'll lose your pack somehow, so know that you can get along with just what's around your neck, on your belt, and in your pockets.
Big knives and hatchets and such are for when you're setting up a base camp, or horseback riding through an area, or 4-wheeling or ATVing, or even canoeing (but even there the weight starts to matter, especially when that portage comes up). Or, maybe, if you're US military and on recon.

But they're really not something you want to lug around on a civilian recreational backpacking trip through your local national forest.
Just my opinion, of course. That and my knees', that is.
