Answer
$\begin{aligned} & F_{A B}=469 \mathrm{lb} \\ & F_{A C}=F_{A D}=331 \mathrm{lb}\end{aligned}$
Work Step by Step
$
\begin{aligned}
& \mathbf{F}_{A D}=F_{A D}\left(\frac{-1 \mathbf{j}+1 \mathbf{k}}{\sqrt{(-1)^2+1^2}}\right)=-0.7071 F_{A D} \mathbf{j}+0.7071 F_{A D} \mathbf{k} \\
& \mathbf{F}_{A C}=F_{A C}\left(\frac{1 \mathbf{i}+1 \mathbf{k}}{\sqrt{1^2+1^2}}\right)=0.7071 F_{A C} \mathbf{i}+0.7071 F_{A C} \mathbf{k} \\
& \mathbf{F}_{A B}=F_{A B}\left(\frac{-0.7071 \mathbf{i}+0.7071 \mathbf{j}+1 \mathbf{k}}{\sqrt{(-0.7071)^2+0.7071^2+1^2}}\right) \\
& =-0.5 F_{A B} \mathbf{i}+0.5 F_{A B} \mathbf{j}+0.7071 F_{A B} \mathbf{k} \\
& \mathbf{F}=\{-800 \mathbf{k}\} \mathrm{lb} \\
& \Sigma \mathbf{F}=\mathbf{0}, \quad \mathbf{F}_{A D}+\mathbf{F}_{A C}+\mathbf{F}_{A B}+\mathbf{F}=\mathbf{0} \\
& \left(-0.7071 F_{A D} \mathbf{j}+0.7071 F_{A D} \mathbf{k}\right)+\left(0.7071 F_{A C} \mathbf{i}+0.7071 F_{A C} \mathbf{k}\right) \\
& +\left(-0.5 F_{A B} \mathbf{i}+0.5 F_{A B} \mathbf{j}+0.7071 F_{A B} \mathbf{k}\right)+(-800 \mathbf{k})=\mathbf{0} \\
& \left(0.7071 F_{A C}-0.5 F_{A B}\right) \mathbf{i}+\left(-0.7071 F_{A D}+0.5 F_{A B}\right) \mathbf{j} \\
& +\left(0.7071 F_{A D}+0.7071 F_{A C}+0.7071 F_{A B}-800\right) \mathbf{k}=\mathbf{0} \\
& \Sigma F_X=0 ; \quad 0.7071 F_{A C}-0.5 F_{A B}=0 \\
& \Sigma F_y=0 ; \quad-0.7071 F_{A D}+0.5 F_{A B}=0 \\
& \Sigma F_q=0 ; \quad 0.7071 F_{A D}+0.7071 F_{A C}+0.7071 F_{A B}-800=0 \\
&
\end{aligned}
$
Solving Eqs:
$
F_{A B}=469 \mathrm{lb} \quad F_{A C}=F_{A D}=331 \mathrm{lb}
$
