Answer
\[
30 \sqrt{5} \mathrm{ \ lb}=\|\vec{F}\|
\]
Work Step by Step
In the figure, we note two forces. The resulting force is
\[
\vec{F}_{2}+\vec{F}_{1}=\vec{F}
\]
where $(60 \mathrm{lb}) \hat{\imath} =\overline{F_{1}} \rightarrow$ positive direction of the x-axis
\[
(301 \mathrm{b}) \hat{\jmath} =\overline {F_{2}} \rightarrow \text { positive direction of the } y \text { -axis }
\]
and then
\[
\begin{aligned}
\vec{F}=\vec{F}_{2}+\vec{F}_{1} &=(30 \mathrm{lb}) \hat{\mathrm{j}} +(60 \mathrm{lb}) \hat{\imath}\\
&=(2 \hat{\imath}+\hat{\jmath})30 \mathrm{lb}=30 \mathrm{lb}\langle 2,1\rangle
\end{aligned}
\]
Thus, we get:
\[
\begin{aligned}
\|\vec{F}\| &=\|30 \mathrm{lb}(2,1)\|=|\langle 2,1\rangle\|30 \mathrm{h}\ \\
&=30 \mathrm{lb} \sqrt{1^{2}+2^{2}}=30 \sqrt{5} \mathrm{lb}
\end{aligned}
\]
