Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?

I. P\(_1\) cos \(\theta_1\) = p\(_1\) cos \(\theta_2\)

II. P\(_3\) = P\(_1\) cos \(\theta_4\)  + P\(_2 cos_2\)

III. P\(_1 \sin \theta_1 = P_2 \sin \theta_2\)