Problem $4$: A force $F$ acts on the end of the beam in the direction shown.

a$.$ Find the component of $F$ in the direction $AB.$ Call this value $F_{AB}.$

b$.$ Find the component of $F$ in the direction perpendicular to $AB.$ Call this value $F_{\text{p}\text{e}\text{r}\text{p}\text{.}}.$

c$.$ For the beam design to be acceptable, neither $F_{AB}$ nor $F_{\text{p}\text{e}\text{r}\text{p}}$ should exceed $2\mathrm{.}0$ kN $.$ What is the largest acceptable magnitude of $F?$