Representing Vectors: Calculating Force & Angle

[FS98]

I recently had a test question where I had to calculate a force on a charged particles from two other charges particles. The answer ended up having an x and a y component. I realized I wasn’t quite sure how to represent that vector. Should I just have written it as something like 5Nx^ + 6Ny^, or should I have solved for the magnitude of the resultant vector and stated the angle that the resultant vector was pointing in?

 

[Nugatory]

Should I just have written it as something like 5Nx^ + 6Ny^, or should I have solved for the magnitude of the resultant vector and stated the angle that the resultant vector was pointing in?

That's two different ways of writing the same thing, so neither is wrong.

If your professor wants you reporting your result one way instead of the other, then of course you'll do it that way... but generally you choose whichever notation is most convenient for the problem at hand. The angle/magnitude form is usually easier to visualize; the component notation is often easier if you have to do more calculations with the vector.