Walker, Halliday & Resnick — Force and Motion-I: Problem 8

8 A 1.50 kg object is subjected to three forces that give it an acceleration \(\vec{a} = -(8.00 \text{ m/s}^2)\hat{i} + (6.00 \text{ m/s}^2)\hat{j}\). If two of the three forces are \(\vec{F}_1 = (30.0 \text{ N})\hat{i} + (16.0 \text{ N})\hat{j}\) and \(\vec{F}_2 = -(12.0 \text{ N})\hat{i} + (8.00 \text{ N})\hat{j}\), find the third force.