Three vectors vec$(a),$vec$(b),$ and vec$(c),$ each have a magnitude of $53\mathrm{.}0m$ and lie in an xy plane. Their directions relative to the positive direction of the $x$ axis are $33\mathrm{.}0,192,$ and $315,$ respectively. What are $($a$)$ the magnitude and $($b$)$ the angle of the vector vec$(a)+$vec$(b)+$vec$(c)($relative to the $+x$ direction in the range of $($:$(-180,180)\},$ and $($c$)$ the magnitude and $($d$)$ the angle of vec$(a)-$vec$(b)+$vec$(c)$ in the range of $(-180,180)?$ What are $($e$)$ the magnitude and $($f$)$ the angle $($in the range of $(-180,180))$ of a fourth vector vec$(d)$ such that $(vec(a)+$vec$(b))-(vec(c)+$vec$(d))=0?$

$($a$)$ Number Unit

$($b$)$ Number Unit

$($c$)$ Number Unit

$($d$)$ Number Unit

$($e$)$ Number Unit

$($f$)$ Number Unit