Question

Three collinear forces,F1=45N west,F2=63N east and an unknown force F3 are applied to an object.The resultant force of the three forces is 12N west.
Show by means of a tail to head method of vector addition how the magnitude of F3 could be found?​

Answer 1

Take east to be the positive direction. Then the resultant force from adding F₁ and F₂ is

F₁ + F₂ = (-45 N) + 63 N = 18 N

which is positive, so it's directed east.

To this we add a third force F₃ such that the resultant is 12 N pointing west, making it negative, so that

18 N + F₃ = -12 N

F₃ = -30 N

So F₃ has a magnitude of 30 N and points west.