Answer
-37 J
Work Step by Step
The force vector in unit vector notation is given by
$\vec{F}=F_{x}\hat{i}+F_{y}\hat{j}$
$=(F\cos\theta)\hat{i}+(F\sin\theta)\hat{j}$
$=(10\,N\cos 150^{\circ})\hat{i}+(10\,N\sin150^{\circ})\hat{j}$
$=(-8.7\,N)\hat{i}+(5.0\,N)\hat{j}$
$\vec{d}=(2.0\,m)\hat{i}-(4.0\,m)\hat{j}$
W= $\vec{F}\cdot\vec{d}=F_{x}d_{x}+F_{y}d_{y}$
$=(-8.7\,N\times2.0\,m)+(5.0\,N\times-4.0\,m)=-37\,J$
