To solve this problem, let's go through the steps to add vector $\mathbf{u} = \langle 2, -5 \rangle$ to the vector $\mathbf{v}$, which is displayed in the graph.

Steps for Vector Addition

1. Determine the coordinates of vector $\mathbf{v}$: To add the vectors graphically, we first need the coordinates of $\mathbf{v}$ (which is not provided directly in the question). We will assume the vector $\mathbf{v}$ has coordinates based on where it ends on the graph. Let’s approximate these coordinates if they're visible.

2. Graphical Addition: To add vector $\mathbf{u}$ to $\mathbf{v}$ graphically, start from the tip (endpoint) of $\mathbf{v}$. From that point, move according to the components of $\mathbf{u}$:

   • Move 2 units to the right (positive $x$-direction).
   • Move 5 units down (negative $y$-direction).

   Mark this new endpoint, which represents the endpoint of the resultant vector $\mathbf{v} + \mathbf{u}$.

3. Resultant Vector in Component Form:

   • Suppose $\mathbf{v} = \langle a, b \rangle$.
   • The resultant vector $\mathbf{v} + \mathbf{u}$ would then be $\langle a + 2, b - 5 \rangle$.

4. Write the Final Answer: Once we know the coordinates of $\mathbf{v}$, we can add the components directly and present the resultant vector.

If you can provide the coordinates for $\mathbf{v}$ from the graph, I can give the exact resultant vector in component form. Let me know if you'd like more assistance on this!

Would you like a detailed explanation of vector addition or have any specific questions?

Related Questions to Expand Understanding:

1. How do you determine the magnitude of a vector?
2. What is the difference between graphical and algebraic vector addition?
3. How can we find the direction of a vector in a plane?
4. What are some real-life applications of vector addition?
5. How does scalar multiplication affect a vector’s direction and magnitude?

Tip:

When performing vector addition, always make sure to account for direction.