Problem $3(10$ pts$)$

Consider Fig. $3$ with $L=100$ N$.$

$($a$)$ Calculate the magnitude of the forces in the two cables and the bar. $(5$ pts$)$

$($b$)$ Express the forces in the cables and the bar in terms of the base $E\{hat(e{)}_1,$hat$(e{)}_2,$hat$(e{)}_3\}.(4$ pts$)$

$($c$)$ Is the bar working in tension or compression? $(1$ pts$)$

Fig. $3$: Note: here the $","$ indicates decimal points, e$.$g$.,5,4m=5\mathrm{.}4m.$