What everybody is saying is valid. This is not something you could or would even want to pull off without permits, plans and engineering. Now that's out of the way.
There are two articles at the UMass Amherst Building and Construction Technology site that you might want to start with:
You will have to work through your own house's dimensions and your local code books to figure the load that your new beam would be carrying.
Like the other responders to your question, I am not clear as to what the new beam is picking up. If it had nothing to do with the porch but was just holding up the rafters coming of the vaulted ceiling in the main house, and if it was the same length or less than the beam in the vaulted ceiling, and if that existing ridge beam was sized correctly, then your new beam might not be any larger than the current ridge beam. But that's a lot of "ifs" to get to a "might."
If the new wall header beam is also carrying half the load of the porch roof system because the porch is also vaulted, then the beam is going to size up from there, and you will have to work through all the tables to figure the load off the porch roof system and add that to load coming off the main house. If the porch is not vaulted and is built with a ridge board instead, then you may not be adding load from the porch at all. More ifs and maybes.
If you did figure all the loads out, you could size the engineered beam using tables available online from beam manufacturers.
The other responders are also calling attention to the fact that it's a lot more than the beam you will have to work through. For starters, it sounds quite likely that you would need some burly footings under the ends of this thing.
Sharpen your pencil, and good luck,
RDG Read Development LLC