During a recent remodel, I came across a 3 inch deep by 5 inch wide bottom notch in a 3x10 (the beams are that old!). I must say, i'm just a diy'er and even I was beside myself that someone would do this to that type of timber, let alone just to route a bathroom VENT HOSE! Anyway, I am going to repair and it and wanted some opinions on the use of dimensional lumber (a 2 x 10 that is 4' 5" wide centered on the notch or perhaps 2 of them) versus using solid 3/4 inch plywood that is 9.5 tall and 4' 5" wide. Everything tells me the dimensional lumber is right, but it tends to be imperfect and in thinking about it I am wondering if a clean sheet of plywood actually may result in a more complete contact surface for the liquid nails and thus a stronger repair by joining more surface area of the three pieces (I would put plywood on both sides of the joist). It feels to me like the adhesive and subsequently the overall contact surface is the real strength in this repair and not the nails that hold the fix in place. As well, my thinking is the plywood would be lighter and thus put little strain on the nails or adhesive just to hold itself in place and so while not as "beefy" as a 2x10, it may actually result in a stronger result with respect to the notch. Again, just a diy'er and may be overthinking this but wanted some opinions?