Answer
$\begin{aligned} & F_{A B}=348 \mathrm{~N} \\ & F_{A C}=413 \mathrm{~N} \\ & F_{A D}=174 \mathrm{~N}\end{aligned}$
Work Step by Step
$
\begin{aligned}
& \mathbf{u}_{A B}=\frac{3 \mathbf{i}+4 \mathbf{j}+0.5 \mathbf{k}}{\sqrt{3^2+4^2+(0.5)^2}}=\frac{3 \mathbf{i}+4 \mathbf{j}+0.5 \mathbf{k}}{\sqrt{25.25}} \\
& \mathbf{u}_{A C}=\frac{-6 \mathbf{i}-3 \mathbf{j}+2.5 \mathbf{k}}{\sqrt{(-6)^2+(-3)^2+2.5^2}}=\frac{-6 \mathbf{i}-3 \mathbf{j}+2.5 \mathbf{k}}{\sqrt{51.25}} \\
& \mathbf{u}_{A D}=\frac{4 \mathbf{i}-3 \mathbf{j}+0.5 \mathbf{k}}{\sqrt{4^2+(-3)^2+0.5^2}}=\frac{4 \mathbf{i}-3 \mathbf{j}+0.5 \mathbf{k}}{\sqrt{25.25}} \\
& \Sigma F_x=0 ; \quad \frac{3}{\sqrt{25.25}} F_{A B}-\frac{6}{\sqrt{51.25}} F_{A C}+\frac{4}{\sqrt{25.25}} F_{A D}=0 \\
& \Sigma F_y=0 ; \quad \frac{4}{\sqrt{25.25}} F_{A B}-\frac{3}{\sqrt{51.25}} F_{A C}-\frac{3}{\sqrt{25.25}} F_{A D}=0 \\
& \Sigma F_z=0 ; \quad \frac{0.5}{\sqrt{25.25}} F_{A B}+\frac{2.5}{\sqrt{51.25}} F_{A C}+\frac{0.5}{\sqrt{25.25}} F_{A D}-20(9.81)=0
\end{aligned}
$
After Solving,
$
\begin{aligned}
& F_{A B}=348 \mathrm{~N} \\
& F_{A C}=413 \mathrm{~N} \\
& F_{A D}=174 \mathrm{~N}
\end{aligned}
$
