1. **State the problem:** Find the direction angle $\theta$ of the vector $\vec{v} = (-3, -10)$ measured from the positive x-axis. 2. **Formula:** The direction angle $\theta$ is given by $$\theta = \tan^{-1}\left(\frac{y}{x}\right)$$ where $x$ and $y$ are the components of the vector. 3. **Calculate the angle:** Here, $x = -3$ and $y = -10$, so $$\theta = \tan^{-1}\left(\frac{-10}{-3}\right) = \tan^{-1}\left(\frac{10}{3}\right)$$ 4. **Evaluate the arctangent:** $$\theta = \tan^{-1}(3.3333) \approx 73.30^\circ$$ 5. **Determine the correct quadrant:** Since both $x$ and $y$ are negative, the vector lies in the third quadrant. The angle from the positive x-axis is $$\theta = 180^\circ + 73.30^\circ = 253.30^\circ$$ 6. **Final answer:** The direction of $\vec{v}$ is approximately $$\boxed{253.30^\circ}$$ This angle is measured counterclockwise from the positive x-axis to the vector $\vec{v}$.