I'm finishing the interior of my garage and will be installing recessed lights in an angled part of the ceiling pictured. I wanted to know if it is OK to drill a 1/2" hole across each ceiling joists (red in photo) to run my wire to each can or should I run the wire to the wall, down through the top and across the wall studs then back up (blue in photo)? Thanks in advance.
More information details would be needed to work out a definitive answer but in general the answer is yes if you keep the hole in the middle 1/3 of the joist depth. The worst thing to do is cut the bottom 1/3 where the joists are in tension and cutting it there will severally reduced the strength and create stress concentrations that will most likely cause cracking over time.
The rafter is weakest where the two different sizes of sistering meet. don't drill near that.
when drilling drill near the top of the middle third of the rafter so that you also hit in the the middle third of the sister. A half-inch hole is tiny and should not significantly reduce the strength of the timber.