Based on the figure, determine the x and y components of the...

Resolving the given vectors into their $x$ and $y$ components:

For vector $\vec{OA}$:
OA_x = 2.0 \cos 30^{}^{{}^{\circ}} = 2.0 \times \dfrac{\sqrt{3}}{2} \approx 1.732 \text{ m}
OA_y = 2.0 \sin 30^{}^{{}^{\circ}} = 2.0 \times \dfrac{1}{2} = 1.0 \text{ m}

For vector $\vec{BC}$:
The vector makes an angle of 60^{}^{{}^{\circ}} with the negative $x$-axis.
BC_x = -1.5 \cos 60^{}^{{}^{\circ}} = -1.5 \times \dfrac{1}{2} = -0.75 \text{ m}
BC_y = 1.5 \sin 60^{}^{{}^{\circ}} = 1.5 \times \dfrac{\sqrt{3}}{2} \approx 1.5 \times 0.866 = 1.299 \text{ m}

For vector $\vec{DE}$:
The vector is directed along the negative $y$-axis.
$DE_x = 0 \text{ m}$
$DE_y = -1.0 \text{ m}$

The $x$-component of the resultant vector is:
$R_x = OA_x + BC_x + DE_x = 1.732 - 0.75 + 0 = 0.982 \text{ m} \approx 0.98 \text{ m}$

The $y$-component of the resultant vector is:
$R_y = OA_y + BC_y + DE_y = 1.0 + 1.299 - 1.0 = 1.299 \text{ m} \approx 1.3 \text{ m}$