Magnitude of forces $F_{AB} =100 N,F_{AC} =150 N,F_{AD}=200 N.$

$\bar {F_{AB}} = F_{AB} .\hat {AB} = 100 × \dfrac {(-1-1)i+(3-0)j+(5-0)k}{\sqrt{(-1-1)^2+(3-0)^2+(5-0)^2} }\\ ∴\bar {F_{AB}} = -32.44 i ̅+48.67 j ̅+81.11 k ̅ \\ \bar {F_{AC}} = F_{AC} .\hat{AC} = 150× \dfrac {(3-1)i+(5-0)j+(7-0)k}{\sqrt{(3-1)^2+(5-0)^2+(7-0)^2}} \\ ∴ \bar {F_{AC}} = 33.96 i ̅+84.92 j ̅+118.89 k ̅ \\ \bar {F_{AD}} = F_{AD} .\hat {AD} = 200× \dfrac {(0-1)i+(4-0)j+(0-0)k}{\sqrt {(0-1)^2+(4-0)^2+(0-0)^2}} \\ ∴ \bar {F_{AD}} = -48.51i ̅+194.03 j ̅ $

Resultant,

$R= \bar {F_{AB}} + \bar {F_{AC}} +F_{AD} \\ R= -46.99 i ̅+327.62 j ̅+200 k ̅$