To solve the problem where you must position points A and B so that the vector AB equals the sum of vectors u (in blue) and v (in red), follow these steps:

1. Understand the vector addition:
   The goal is to place the green vector AB such that it visually represents:
   $\vec{AB} = \vec{u} + \vec{v}$
   The vector sum combines the directions and magnitudes of u and v.

2. Align vectors u and v:

   • Start at a point (for instance, A).
   • Use u (blue vector) first, then place v (red vector) starting at the tip of u.
   • The resulting vector from the start of u to the tip of v is the sum $\vec{u} + \vec{v}$.

3. Position points A and B:

   • Place A at a fixed starting position (where you want to begin).
   • Use the grid to determine the endpoint B after visually adding u and v.

Breakdown:

• Start at A.
• Follow the direction and length of u.
• From the tip of u, move in the direction and length of v.
• The endpoint gives you the correct position for B.

Let me know if you need a visual step-by-step explanation or confirmation on your adjustments.

Related Questions:

1. How do you calculate the resultant vector algebraically?
2. What are the rules for vector addition (parallelogram method vs. tip-to-tail)?
3. How can vectors be represented in component form on a grid?
4. How do you measure vector magnitudes and directions on a graph?
5. What is the significance of vector addition in physics or engineering?

Tip: Always follow the tip-to-tail method to add vectors graphically.