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

A 2.00 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.