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draw force w which has twice the strength of and is the opposite to A

To draw a vector \( \mathbf{W} \) that has twice the strength of vector \( \mathbf{A} \) and is in the opposite direction, we need to consider the following steps:

1. **Determine the direction of \( \mathbf{A} \):** 
   From the grid, we can see that vector \( \mathbf{A} \) points towards the top-right quadrant of the grid.

2. **Opposite direction:** 
   The opposite direction would be pointing towards the bottom-left quadrant. This means \( \mathbf{W} \) will go in the opposite direction from \( \mathbf{A} \).

3. **Twice the strength:** 
   To represent double the strength, we need to make the vector twice as long as \( \mathbf{A} \). If \( \mathbf{A} \) moves a certain number of grid units from its origin, \( \mathbf{W} \) will move twice that number in the opposite direction.

Let's outline these steps on the grid:

- Locate the end of vector \( \mathbf{A} \).
- Draw vector \( \mathbf{W} \) starting from the origin, pointing in the exact opposite direction as \( \mathbf{A} \), and extending to twice the length of \( \mathbf{A} \).

Let me know if you'd like a detailed breakdown of the calculations or any other clarifications. 

Here are 5 follow-up questions:

1. What is the exact grid length of vector \( \mathbf{A} \)?
2. How do we measure the strength (or magnitude) of vectors on this grid?
3. Would you like to analyze the directions of other vectors \( \mathbf{B} \) or \( \mathbf{C} \)?
4. Can I help you calculate the sum of any two vectors shown on the grid?
5. Would you like to explore vector operations such as dot product or cross product?

**Tip:** When working with vectors, the length (or magnitude) is crucial for determining strength, while direction determines orientation in the plane.

Learn how to draw a vector with twice the strength and in the opposite direction of a given vector A. This vector problem involves understanding vector magnitude and direction, suitable for students in Grades 10-12.

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