Two vectors lying in the $x-y$ plane are defined by their magnitudes and direction angles, as shown in the figure below. Vector vec$(A)$ has magnitude $A=1611N$ and angle ${}_A=50,$ and vector vec$(B)$ has magnitude $B=1631N$ and angle ${}_B=60.$ Using Cartesian components, determine the magnitude and direction angle of the following three vectors:

$($a$)$ vec$(S{)}_V=$vec$(A)+$vec$(B)$

$($b$)$ vec$(D{)}_{V1}=$vec$(A)-$vec$(B)$

$($c$)$ vec$(D{)}_{V2}=$vec$(B)-$vec$(A)$

Note: Express your answers for $$ between $-180$ and $180$ relative to the $+x-$axis.

$\backslash$table$[[S_V=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),$N$,(3)],[{}_{S_V}=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),,(3)],[D_{V1}=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),$N$,(3)],[{}_{D_{V1}}=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),,(3)],[D_{V2}=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),$N$,(3)],[{}_{D_{V2}}=,$number $($rtol $=0\mathrm{.}01,$ atol $=1e-05),,(3)]]$