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

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 \(F_x\).