Given a T$-$frame with a pinned support in $\backslash ($ A $\backslash )$ and a simple roller bearing at $\backslash ($ B $\backslash ),$ permitting motion at $\backslash (45^\{\backslash$circ$\}\backslash ).$ A vertical force $\backslash ($ P $\backslash )$ is acting at the tip in $\backslash ($ D $\backslash ).$

$1)$ Determine the reaction components. Represent the inclined reaction in $\backslash ($ B $\backslash )$ by its horizontal and vertical components. $(1$p$)$

$2)$ Determine and draw the distribution of internal forces $\backslash ($ N$,$ Q $\backslash )$ and $\backslash ($ M $\backslash ).(3$p$)$

$3)$ Isolate the joint $\backslash ($ C $\backslash )$ and verify force and moment equilibrium. $(1$p$)$