A particle is acted on by two torques about the origin: `vectau_(1)` has a magnitude of `2.0N*m` and is directed in the positive direction of the x axis, and `vectau_(2)` has a magnitude of `3.0N*m` and is directed in the nagative direction of the y axis. In unit-vector notation, find `vec(dl)//dt`, where `vecl` is the angular momentum of the particle about the origin.

Explanation

To solve the problem, we need to find the time rate of change of angular momentum, denoted as \( \frac{d\vec{L}}{dt} \), which is equal to the net torque acting on the particle.

### Step-by-step Solution:

1. **Identify the Given Torques:**
- The first torque \( \vec{\tau}_1 \) has a magnitude of \( 2.0 \, \text{N}\cdot\text{m} \) and is directed along the positive x-axis. In unit vector notation, this can be expressed as:
\[
\vec{\tau}_1 = 2.0 \, \text{N}\cdot\text{m} \, \hat{i}
...