Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 22

22 A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector $\vec{r} = (2.00 \text{ m})\hat{i} - (3.00 \text{ m})\hat{j} + (2.00 \text{ m})\hat{k}$, the force is given by $\vec{F} = F_x \hat{i} + (7.00 \text{ N})\hat{j} - (6.00 \text{ N})\hat{k}$ and the corresponding torque about the origin is $\vec{\tau} = (4.00 \text{ N}\cdot\text{m})\hat{i} + (2.00 \text{ N}\cdot\text{m})\hat{j} - (1.00 \text{ N}\cdot\text{m})\hat{k}$. Determine $F_x$.