1. **Problem Statement:** We are given the vector $\mathbf{v} = [-1, 3]$. We need to sketch this vector and find its length. 2. **Formula for Length of a Vector:** The length (or magnitude) of a vector $\mathbf{v} = [x, y]$ in 2D is given by the formula: $$\text{length} = \sqrt{x^2 + y^2}$$ 3. **Apply the formula:** For $\mathbf{v} = [-1, 3]$, we have: $$x = -1, \quad y = 3$$ 4. Calculate the length: $$\text{length} = \sqrt{(-1)^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10}$$ 5. **Interpretation:** The length of the vector is $\sqrt{10}$, which is approximately 3.162. 6. **Sketching the vector:** The vector starts at the origin $(0,0)$ and points to the coordinate $(-1, 3)$ in the Cartesian plane. It points left 1 unit and up 3 units. **Final answer:** The length of the vector $[-1, 3]$ is $\sqrt{10}$.