Ta có hợp lực: \(\overrightarrow F = \overrightarrow {{F_1}} + \overrightarrow {{F_2}} \)
Độ lớn: \({F^2} = F_1^2 + F_2^2 + 2{F_1}{F_2}cos\alpha \)
a) \(\left( {\widehat {\overrightarrow {{F_1}} ;\overrightarrow {{F_2}} }} \right) = {0^0}\)
\(F = {F_1} + {F_2} = 20 + 20 = 40N\)
b) \(\left( {\widehat {\overrightarrow {{F_1}} ;\overrightarrow {{F_2}} }} \right) = {60^0}\)
\(\begin{array}{l}{F^2} = F_1^2 + F_2^2 + 2{F_1}{F_2}cos\alpha \\ = {20^2} + {20^2} + 2.20.20.cos{60^0}\\ = 1200\\ \Rightarrow F = 20\sqrt 3 N\end{array}\)
c)
\(\left( {\widehat {\overrightarrow {{F_1}} ;\overrightarrow {{F_2}} }} \right) = {90^0}\)
\(F = \sqrt {F_1^2 + F_2^2} = \sqrt {{{20}^2} + {{20}^2}} = 20\sqrt 2 N\)
d) \(\left( {\widehat {\overrightarrow {{F_1}} ;\overrightarrow {{F_2}} }} \right) = {120^0}\)
\(\begin{array}{l}{F^2} = F_1^2 + F_2^2 + 2{F_1}{F_2}cos\alpha \\ = {20^2} + {20^2} + 2.20.20.cos{120^0}\\ = 400\\ \Rightarrow F = 20N\end{array}\) e) \(\left( {\widehat {\overrightarrow {{F_1}} ;\overrightarrow {{F_2}} }} \right) = {180^0}\)
\(F = {F_1} - {F_2} = 20 - 20 = 0N\)
