Question Number 65170 by Rio Michael last updated on 25/Jul/19
$${three}\:{forces}\:{F}_{\mathrm{1}} ,\:{F}_{\mathrm{2}} \:{and}\:{F}_{\mathrm{3}} \:{acts}\:{through}\:{the}\:{points}\:{with}\:{position}\:{vectors} \\ $$$$\boldsymbol{{r}}_{\mathrm{1}} ,{r}_{\mathrm{2}} \:{and}\:{r}_{\mathrm{3}} \:{respectively}\:{where} \\ $$$$\:{F}_{\mathrm{1}} \:=\left(\mathrm{3}{i}\:−\mathrm{2}{j}−\mathrm{4}{k}\right){N},\:\:\:{r}_{\mathrm{1}} =\:\left({i}\:+{k}\right){m} \\ $$$${F}_{\mathrm{2}} =\left(−{i}+{j}\right){N},\:\:{r}_{\mathrm{2}} =\left({j}+{k}\right){m} \\ $$$${F}_{\mathrm{3}} =\left(−{i}+\mathrm{4}{k}\right){N},\:{r}_{\mathrm{3}} =\left({i}+{j}+{k}\right){m} \\ $$$${a}.\:{show}\:{that}\:{this}\:{system}\:{does}\:{not}\:{reduce}\:{to}\:{a}\:{single}\:{force}. \\ $$$$\:{When}\:{a}\:{fourth}\:{force}\:{F}\:{is}\:{added},\:{the}\:{system}\:{of}\:{forces}\:{is}\:{in}\:{equilibrium} \\ $$$${b}.\:{Show}\:{that}\:{F}\:{acts}\:{through}\:\:{the}\:{point}\:{with}\:{vectors}\:\left(\mathrm{3}{k}\right){m}. \\ $$