Walker, Halliday & Resnick — Force and Motion-I: Problem 32

32 Figure 5-29 shows an overhead view of a 0.0250 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force $\vec{F}_1$ has a magnitude of 6.00 N and is at $\theta_1 = 30.0^\circ$. Force $\vec{F}_2$ has a magnitude of 7.00 N and is at $\theta_2 = 30.0^\circ$. In unit-vector notation, what is the third force $\vec{F}_3$ if the lemon half (a) is stationary, (b) has the constant velocity $\vec{v} = (13.0\hat{i} - 14.0\hat{j})\text{ m/s}$, and (c) has the varying velocity $\vec{v} = (13.0t\hat{i} - 14.0t\hat{j})\text{ m/s}$, where $t$ is time?