(Solved): Two vectors lying in the \( \mathrm{x} \)-y plane are defined by their magnitudes and direction ang ...

Two vectors lying in the \( \mathrm{x} \)-y plane are defined by their magnitudes and direction angles, as shown in the figure below. Vector \( \vec{A} \) has magnitude \( A=1498 \mathrm{~N} \) and angle \( \theta_{A}=55^{\circ} \), and vector \( \vec{B} \) has magnitude \( B=1672 \mathrm{~N} \) and angle \( \theta_{B}=80^{\circ} \). Using Cartesian components, determine the magnitude and direction angle of the following three vectors: (a) \( \vec{S}_{V}=\vec{A}+\vec{B} \) (b) \( \vec{D}_{V 1}=\vec{A}-\vec{B} \) (c) \( \vec{D}_{V 2}=\vec{B}-\vec{A} \) Note: Express your answers for \( \theta \) between \( -180^{\circ} \) and \( 180^{\circ} \) relative to the \( +x \)-axis.