The $6-$m pole $\backslash ($ A B C $\backslash )$ is acted upon by a $465-$N force, $\backslash (\backslash$mathbf$\{$P$\}\backslash ),$ as shown in the figure. The pole is held by a ball$-$and$-$socket joint at $\backslash ($ A $\backslash )$ and by two cables $\backslash ($ B D $\backslash )$ and $\backslash ($ B E $\backslash ).$

For $\backslash ($ a$=3\backslash$mathrm$\{$~m$\}\backslash ),$ determine the tension in each cable and the reaction at $\backslash ($ A $\backslash ).($Include a minus sign if necessary.$)$

The tension in cable $\backslash ($ B D $\backslash )$ is

N $.$

The tension in cable $\backslash ($ B E $\backslash )$ is

N $.$

The reaction at $\backslash ($ A $\backslash )$ is $($

$\backslash (\backslash$mathrm$\{$N$\})\backslash$mathbf$\{$i$\}+(\backslash )$

$\backslash (\backslash$mathrm$\{$N$\})\backslash$mathbf$\{$j$\}+(\backslash )$

N$).$