$\overline F_{AB}=100\ \dfrac{\overline{AB}} {|\overline{AB}|}=\dfrac{100(-2\hat{a} +3\hat j+5\hat k)}{\sqrt{2^2+3^2+5^2}} =-32.47\ \hat i+48.7\ \hat j+81.17\ \hat k\ (N)$

$\overline F_{AC}=150\ \dfrac{\overline{AC}} {|\overline{AC}|}=\dfrac{150(2\hat{i} +5\hat j+7\hat k)}{\sqrt{2^2+5^2+7^2}} =33.98\ \hat i+84.94\ \hat j+118.9\ \hat k\ (N)$

$\overline F_{AD}=200\ \dfrac{\overline{AD}} {|\overline{AD}|}=\dfrac{200(-\hat{i} +4\hat j)}{\sqrt{1^2+4^2}} =-48.5\ \hat i+194\ \hat j\ \ (N)$

Resultant Force

$\overline R=\overline F_{AB}+\overline F_{AC}+\overline F_{AD}=-47\hat …