Relatia vectoriala este: [tex] \vec{R}=\vec{F_1}+\vec{F_2} [/tex]
Rezultanta este maxima cand fortele au aceeasi orientare (aceeasi directie si acelasi sens): [tex] R_{\max}=F_1+F_2 [/tex].
Rezultanta este maxima cand fortele au orientari opuse (aceeasi directie, sens opus): [tex] R_{\min}=F_1-F_2 [/tex] (luam cazul [tex] F_1>F_2 [/tex])
[tex] F_2=R_{\max}-F_1\implies R_{\min}=F_1-R_{\max}+F_1=2F_1-R_{\max}\\ \\ \implies F_1=\dfrac{R_{\max}+R_{\min}}{2}=18N\implies F_2=13 N [/tex]
Aplici teorema cosinusului:
[tex] R^2=F_1^2+F_2^2-F_1F_2\cos(180-\alpha)[/tex]
Numeric, [tex] R=\sqrt{F_1^2+F_2^2-F_1F_2\cos(60^\circ)}=19,3907194297N [/tex]
