$3-$D Equilibrium $(25$ points$)$

The bracket ABC is supported by two ball$-$and$-$socket joints at A and C and a cable that is passed through a loop at B and attached to the wall at E and F $.$

$($a$)(5$ points$)$ Draw the bracket body diagram.

$($b$)(5$ points$)$ Express the tension force in the BE portion of the cable in vector notation in terms of the tension magnitude $T($Hint: vec$(T{)}_{BE}=T(a_x(vec(i))+a_x(vec(i))+a_x(vec(i)))).$

$($c$)(5$ points$)$ Express the tension force in the BF portion of the cable in vector notation in terms of the tension magnitude $T($Hint: vec$(T{)}_{BF}=T(b_x(vec(i))+b_z(vec(i))+b_z(vec(i)))).$

$($d$)(5$ points$)$ Identify and write one equation to find $T$ if P is given.

$($e$)(5$ points$)$ Evaluate $($d$)P=10N.$