A 3.0 kg particle-like object moves in a plane with velocity components `v_(x)=30m//sandv_(y)=60m//s` as is passes through the point with (x, y) coordinates of (3.0, -4.0) m. Just then, in unit vector notation, what is its angular momentum relative to (a) the origin and (b) the point located at (-2.0, -2.0) m?

Explanation

To solve the problem, we need to calculate the angular momentum of a particle-like object moving in a plane relative to two different points. The object has a mass of 3.0 kg and velocity components \( v_x = 30 \, \text{m/s} \) and \( v_y = 60 \, \text{m/s} \). The coordinates of the object at the moment of interest are \( (3.0, -4.0) \, \text{m} \).

### Part (a): Angular Momentum Relative to the Origin

1. **Determine the position vector \( \mathbf{r} \) relative to the origin:**
\[ \mathbf{r} = 3 \hat{i} - 4 \hat{j} \]
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