Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 32

32 A particle is acted on by two torques about the origin: $\vec{\tau}_1$ has a magnitude of $2.0 \text{ N}\cdot\text{m}$ and is directed in the positive direction of the $x$ axis, and $\vec{\tau}_2$ has a magnitude of $3.0 \text{ N}\cdot\text{m}$ and is directed in the negative direction of the $y$ axis. In unit-vector notation, find $d\vec{L}/dt$, where $\vec{L}$ is the angular momentum of the particle about the origin.