A particle P is acted by three coplanar forces as shown in the figure. 

Find the force needed to prevent the particle P from moving. (take, $\sqrt{3}=1.7$)

Let applied force ${\text{F}}_{\text{4}}{\text{=F}}_{\text{x}}\widehat{\text{i}}{\text{+F}}_{\text{y}}\widehat{\text{j}}$

To  prevent the particle P from moving . net force on the particle will be zero.

$\therefore \sum {\text{F}}_{\text{x}}\text{=0}$ Or  

${\text{∴∑F}}_{\mathrm{x}}={\mathrm{F}}_{\mathrm{x}}+150+200\cos {30}^0=0\Rightarrow {\mathrm{F}}_{\mathrm{x}}=-320$ 

And  $200\sin {30}^{\mathrm{0}}-100+{\mathrm{F}}_{\mathrm{y}}=0\Rightarrow {\mathrm{F}}_{\mathrm{y}}=0$

Therefore 

${\mathrm{F}}_{\mathrm{4}}=-320\widehat{\mathrm{i}}$ which is opposite to ${\mathrm{F}}_1$