I want to take two 3/4" planks: 2’ x 5’, and place them edgewise in a ‘X’ shape. So in the middle of each plank, I want to cut a 3/4" wide notch that’s 1 foot long. That way, I can slide the two notches over each other and get what I want.
I can easily use a circular saw to cut a pair of parallel lines 1’ down the plank - those will be the outside edges of my notch. But how do I cleanly cut ACROSS the notch at the bottom?
A good sharp 3/4"chisel should do the trick once you’ve sawed the parallel lines.
Maybe I’m misreading your question, but it seems to me that your best bet would be a router. You can easily set the depth for the notch and there are any number of available bits to give you whatever caut profile you want–probably square in this case.
…or you could use a wood drill then chisel the remainder.
I don’t think the chisel is going to be your friend here. Cutting a sheet of plywood with a chisel is not easy. It might work but you will have to go very slowly to avoid chipping.
You might be better off using a coping saw blade and a pair of vise grips. The frame of the coping saw isn’t big enough to make across the distance you need, and a keyhole saw has too large a blade.
I was assuming the OP didn’t have a router or other expensive tools, Q.E.D..
a router would work well, you’d still need to clean up the edges where the radius doesn’t reach, a simple razor knife would suffice for that as well as a chisel.
Routers aren’t all that expensive. I don’t know how much woodworking Bricker does, but if it’s any kind of often, I’d say go buy one. I loves my router!
Lots of different ways to do it. One approach would be to take a 3/4" Forstner or spade bit and drill a hole 3/8" from the bottom of your notch. Then clean up the corners with a chisel or a small handsaw (keyhole saw would work). Or you could just make the cut with a jig saw, although it might be a bit sloppy.
You don’t want to make the side cuts all the way with a circular saw because a circular saw will not cut to a line – the edge of the cut will be slightly curved.
I was assuming that by ‘planks’ the op was talking about solid wood rather than ply…
A router would do the trick fine, but the easiest low-tech option is to drill a few holes then use a chisel (or as MikeG suggests a sharp knife) to clean up.
If you can justify only one good woodworking tool, I’d go for a Rotozip. As a big brother to the moto-tool, it’s great for cutting slots, light routing, and generally turning 3/4" inch wood into things that you can use.
Solid wood, not ply, is contemplated here.
I don’t mind spending a little money to buy the right tool for the job.
You can get a router attachment for the Dremel Moto Tool, I assume there’s a similar one available for the Rotozip?
How many are you making? If it’s a one off, run the circular saw just to the line, flip the piece over and do the same, then clean up with a chisel. If you are doing a production run, a router is the way to go, you can make up a little jig, and zip right through them!
I think you could work the end out with a jig saw by turning in and going to just the edge chip by chip. Leave any stray material and clean it out with a small file, blade or other simple tool.
I’ve made dozen of these types of notches. At the bottom, you wonder how to clean it up. A jig saw can do it when the edge is marked well.
Push the blade to the end on both side, then come back from different angles to the edge until you can turn the blade sqaure to the edge or most of the material is gone. A 3/4 notch should afford you decent turning once the balde is inside the notch area to clean it out. I’d make a very square end with a jig saw.
My first though was also that of a router but here’s another suggestion. If you have a table saw and want to make a number of these cuts, a Dado blade set might be feasible. In essence, you’re stacking a number of different sized saw blades together on your table saw to add up to the desired thickness of the notch. Then you just dial the blade up or down to get the desired depth of cut and run your boards down the fence. I believe I paid about $80 for a set ten years ago, so you’ll likely use this method only if it’s for a fair amount of work to be done.
I would probably make two cuts with the circular or table saw and then make the cross cut with a jigsaw if you could get it in there or a chisel. But the proper tool is a router. I would go for a full size router - looks like a giant orbital sander - rather than the dremel which is pretty small. I’m thinking of the dremel multi-tool I’ve seen on TV.
I’ve reread your OP and misinterpreted your intent. The Dado could be used if you wanted to groove out a 3/4" notch, but probably isn’t appropriate for what you’re doing. Sorry about that.
I don’t think he needs to go over the top. A simple jigsaw will do, and someone mentioned a coping saw.
Nothing elaborate is being built, he just has to finish off the last 3/4" cross cut. Dados and routers require set up and $, and both are overkill.
A simple jig saw or coping saw is just fine. No arguing they could work, but let us focus on what we are doing here: two 3/4" cross cuts are all that remain.
With solid wood, I’d probably use a table saw to cut the sides of the notch, stopping short so that the saw doesn’t go past the end on the bottom side. Then, I’d cut the sides to the bottom of the notch with a hand saw.
For the end, I’d probably cut the wood short somehow, then mark the line by cutting hard with a knife. Then, I’d chisel the waste out with a (sharp) mortising chisel, working from both sides and taking my time. I’d finish by using a (sharp) chisel to clean up where I used the handsaw.
On the other hand, anybody with any common sense would realize that the notch will not be seen, so they would leave all the chisels in their drawer and just rout out the end with a router, rounding the other piece to fit with a file.
Common sense and carpenters in the same sentence? It is to laugh! 
I was taught by a super persnickety German cabinetmaker who taught me that I should exercise the same level of workmanship on those parts of a project that will never be seen as on the visible parts. It makes things a bit slower but I know that every part of anything I make is well done, and I have had occasion to take apart older furniture and the same thing applied back in the day.
But come to think of it, a good rough wood rasp might be all you need.