To solve this question, we need to find the vector that represents $\mathbf{V} - \mathbf{U}$.

Steps to solve:

1. Vector Subtraction: The expression $\mathbf{V} - \mathbf{U}$ can be understood as the sum of $\mathbf{V}$ and the opposite of $\mathbf{U}$. So, $\mathbf{V} - \mathbf{U}$ is equivalent to $\mathbf{V} + (-\mathbf{U})$, where $-\mathbf{U}$ is the vector $\mathbf{U}$ with its direction reversed.

2. Graphical Analysis:

   • Identify the vector $\mathbf{V}$ on the diagram. It points downward and to the left.
   • Identify the vector $\mathbf{U}$, which points upwards and to the right.
   • Reverse the direction of vector $\mathbf{U}$ to get $-\mathbf{U}$. This new vector points downwards and to the left (opposite of $\mathbf{U}$).

3. Adding Vectors: Now, add $\mathbf{V}$ and $-\mathbf{U}$. Since both point in similar directions (downwards and leftwards), the resultant vector will be longer and should follow the same general direction as these vectors combined.

From the diagram, it seems the vector $\mathbf{B}$ aligns with the direction and magnitude expected from the vector sum $\mathbf{V} - \mathbf{U}$.

Conclusion:

The vector that represents $\mathbf{V} - \mathbf{U}$ is most likely (B) $\mathbf{B}$.

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Would you like more details on this process or an explanation of vector addition?

Here are 5 related questions for deeper understanding:

1. What are the properties of vectors that allow for addition and subtraction?
2. How do we find the magnitude and direction of a resultant vector after subtraction?
3. Why is reversing the direction of a vector equivalent to negating it?
4. How would the result differ if the vectors $\mathbf{V}$ and $\mathbf{U}$ were perpendicular instead of having similar directions?
5. Can vector subtraction be performed by breaking the vectors into their components?

Tip: Always ensure you visualize the direction and magnitude of vectors when performing vector operations graphically.