It's been a while since I've worked with vectors. Let's say you have two forces (see the diagram), and you would like to find the resultant force vector. The blue line in the diagram represents the plumb line. I have no trouble finding the magnitude of the resultant (178.9N), and I was able to find the direction (75.1 degrees south of east). However, I couldn't figure out a way to find the direction without breaking each vector into components, which I think is more complicated than it needs to be. Is there a way to find the direction of the resultant vector without using the components?

Question

It's been a while since I've worked with vectors.  Let's say you have two forces (see the diagram), and you would like to find the resultant force vector.  The blue line in the diagram represents the plumb line.  I have no trouble finding the magnitude of the resultant (178.9N), and I was able to find the direction (75.1 degrees south of east).  However, I couldn't figure out a way to find the direction without breaking each vector into components, which I think is more complicated than it needs to be.  Is there a way to find the direction of the resultant vector without using the components?

anonymous · Answer

attachment

phi · Answer

breaking the vectors into components (x and y or N and E) is the way to do this in general.  Maybe for special cases there are faster ways... e.g. 90 degree angles

anonymous · Answer

Yeah, that's how I found the direction, but I couldn't find another way to do it WITHOUT breaking it into components :(