Hello, leinadwerdna!
Do you know how to write vectors and add vectors?
An object $\displaystyle P$ is acted upon by 3 coplanar forces.
One force is 100 pounds due south,
another is 150 pounds due east
and the third is 200 pounds 30° north of east.
What is the force needed to prevent $\displaystyle P$ from moving? Code:
w
*
200 *
*
P * 30°
o       * v
 150
100 

*
u
We have: .$\displaystyle \begin{array}{ccc} \vec u &=& \langle 0,\:\text{}100\rangle \\
\vec v &=& \langle 150,\:0\rangle \\
\vec w &=& \langle 100\sqrt{3},\:100\rangle \end{array}$
The resultant vector is: .$\displaystyle \vec u + \vec v + \vec w \;=\;\langle 250\sqrt{3},\:0\rangle$
$\displaystyle P$ is moving directly east with a force of $\displaystyle 250\sqrt{3}$ pounds
To prevent movement, $\displaystyle 250\sqrt{3}$ pounds of force must be applied directly west.
. . The applied vector would be: .$\displaystyle \langle \text{}250\sqrt{3},\:0\rangle$