I like to think that I understand this vector math stuff fairly well, but this problem has me totally stumped… I’ve had a few “eureka!” moments, but none turned out to be right.

A collar that can slide on a vertical rod is subjected to the three forces shown. Determine (a) the value of the angle beta for which the resultant of the three forces is horizontal, (b) the corresponding magnitude of the resultant.

I’ve changed the numbers on the vectors so just giving me an answer doesn’t help at all. If someone could explain what the process is that’d be great. Any ideas?

I think we can assume that since the two non-vertical vectors are the same distance from the nearest axis (angle beta) that they are 90 degrees apart, but I can’t seem to get a hold of where to go after that.