Answer
$F=52.1 \mathrm{lb}$
Work Step by Step
$\begin{aligned} & \mathbf{F}_C=F \frac{(4 \mathbf{j}-6 \mathbf{k})}{\sqrt{4^2+(-6)^2}}=0.5547 F \mathbf{j}-0.8321 F \mathbf{k} \\ & \mathbf{F}_A=\mathbf{F}_B=\mathbf{F}_C \\ & F_{R z}=\Sigma F_z ; \quad 130=3(0.8321 F) \\ & F=52.1 \mathrm{lb}\end{aligned}$
