# How to Find the Magnitude of Force and Direction

Give me some tips on how I can find the magnitude of $$F_3$$. The hint maybe is the angle of inclination of w axis such that the force components are equal along that axis, my instructor once told me. However, I can't still figure it out on how to solve for that angle.

The problem stated that $$F_1$$ is resolved in u and v axis, $$F_2$$ is resolved in v and w axis, while the $$F_3$$ is resolved in w and u axis. It is also stated in the problem that the components of $$F_1$$ and $$F_2$$ are equal along the v axis, the components of $$F_2$$ and $$F_3$$ are equal along the w axis, and the components of $$F_1$$ and $$F_3$$ are equal along the u axis.

• Can you include the original problem statement? Getting it 'second hand' risks translation errors Mar 4, 2021 at 7:52
• Hello, I already edit my entry. The original problem is now included in an image form. Mar 4, 2021 at 8:10
• Please keep the figure in the text of the problem (not as an external link). Mar 4, 2021 at 8:19

Assuming equilibrium, $$\vec{F_1} + \vec{F_2} + \vec{F_3} = 0$$ . We have: $$\vec{F_1} = \vec{{F_1}_u} + \vec{{F_1}_v}$$ $$\vec{F_2} = \vec{{F_2}_v} + \vec{{F_2}_w}$$ $$\vec{F_3} = \vec{{F_3}_w} + \vec{{F_3}_u}$$ And the problem states that: $$\color{red}{\vec{{F_1}_v}} = \color{red}{\vec{{F_2}_v}}$$ $$\color{blue}{\vec{{F_2}_w}} = \color{blue}{\vec{{F_3}_w}}$$ $$\color{green}{\vec{{F_3}_u}} = \color{green}{\vec{{F_1}_u}}$$ So we can rewrite the equilibrium condition as: $$\color{green}{\vec{{F_1}_u}} + \color{red}{\vec{{F_1}_v}} + \color{red}{\vec{{F_2}_v}} + \color{blue}{\vec{{F_2}_w}} + \color{blue}{\vec{{F_3}_w}} + \color{green}{\vec{{F_3}_u}} = 0$$ Or: $$\color{green}{\vec{{F_1}_u}} + \color{red}{\vec{{F_1}_v}} + \color{blue}{\vec{{F_2}_w}} = 0$$ Which leads to: $$\vec{{F_2}_w} = - \vec{F_1}$$ The rest of the solution is left as an exercise for the interested reader.
• @Aiden That is an important question. If the forces are not in equilibrium then their resultant will not be zero, and the above solution will change. Unless we know the resultant vector (call it $\vec{F_R}$) , we won't have enough information to solve the problem because our calculations will end in $\vec{{F_2}_w} = \vec{F_R} - \vec{F_1}$ . With both $\vec{{F_2}_w}$ and $\vec{F_R}$ unknown, this equation will have infinitely many answers. Mar 4, 2021 at 13:56