Answer
$-161.6x-180y\,N$
Magnitude $=241.82 \,N$
$\theta=48.06^{\circ}$ with respect to Negative direction of x-axis.
Work Step by Step
For the box to be stationary,
$F_{1}+F_{2}+F_{3}=0$
$F_{3}=-F_{1}-F_{2}$
$F_{1}=100cos30^{\circ}x+100sin30^{\circ}y=86.6x+50y\,N$
$F_{2}=150cos60^{\circ}x+150sin60^{\circ}y=75x+130y\,N$
$F_{3}=-F_{1}-F_{2}=-161.6x-180y\,N$
Magnitude of $F_{3}=241.82 \,N$
$\theta=48.06^{\circ}$ with respect to Negative direction of x-axis.
