Hợp lực \(F\) lên chất điểm \(A\) là :
\(\overrightarrow{F}=\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\)
\(\Rightarrow F^2=\left(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\right)^2\)
\(\Rightarrow F^2=a^2+b^2+c^2+2\left(\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}\right)\)
\(\Rightarrow F^2=a^2+b^2+c^2+2\left(ab.cos45^o+bc.cos45^o+ca.cos90^o\right)\)
\(\Rightarrow F^2=a^2+b^2+c^2+2\left(ab.\dfrac{\sqrt{2}}{2}+bc.\dfrac{\sqrt{2}}{2}+ca.0\right)\)
\(\Rightarrow F^2=a^2+b^2+c^2+b\sqrt{2}\left(a+c\right)=2.10^2+15^2+10\sqrt{2}\left(10+15\right)=425+250\sqrt{2}\)
\(\Rightarrow F=\sqrt{425+250\sqrt{2}}\approx27,9\left(N\right)\)