1. **State the problem:** Find the magnitude and direction of the vector $\begin{pmatrix}5 \\ 2\end{pmatrix}$. 2. **Magnitude formula:** The magnitude $|\mathbf{v}|$ of a vector $\mathbf{v} = \begin{pmatrix}x \\ y\end{pmatrix}$ is given by: $$|\mathbf{v}| = \sqrt{x^2 + y^2}$$ 3. **Calculate magnitude:** Substitute $x=5$ and $y=2$: $$|\mathbf{v}| = \sqrt{5^2 + 2^2} = \sqrt{25 + 4} = \sqrt{29}$$ 4. **Direction formula:** The direction $\theta$ (angle with the positive x-axis) is: $$\theta = \tan^{-1}\left(\frac{y}{x}\right)$$ 5. **Calculate direction:** Substitute $x=5$ and $y=2$: $$\theta = \tan^{-1}\left(\frac{2}{5}\right)$$ 6. **Evaluate direction:** Using a calculator or approximation: $$\theta \approx 21.8^\circ$$ **Final answers:** - Magnitude: $\sqrt{29}$ - Direction: approximately $21.8^\circ$ from the positive x-axis.